The graph of linear function k passes through the points(-7,0) and (1,8). Which statement must be true
Answers
The slope of the graph of k is -4/3.
The graph of k passes through the point (-1,-8).
The zero of k is 7
The x-intercept of the graph of k is -7.
Answers
Answer:
✅The x-intercept of the graph of k is -7.
Step-by-sep explanation:
Graph the equation of the line that passes through the points, (-7, 0) and (1, 8) by first generating an equation, and then using the equation of the function to plot the graph.
To find the equation, we need to calculate the slope, m, and y-intercept, b.
✅Using points (-7, 0) and (1, 8), the slope of the line is:
[tex] m = \frac{y_2 - y_1}{x_2 -x_1} = \frac{8 - 0}{1 -(-7)} = \frac{8}{8} = 1 [/tex]
Substitute x = 1, y = 8, m = 1 into [tex] f(x) = mx + b [/tex] to find the y-intercept, b, of the function. (Note: f(x) is same as variable y).
[tex] 8 = 1(1) + b [/tex]
[tex] 8 = 1 + b [/tex]
Subtract 1 from each side
[tex] 8 - 1 = b [/tex]
[tex] 7 = b [/tex]
[tex] b = 7 [/tex]
Substitute m = 1 and b = 7 into [tex] f(x) = mx + b [/tex]
The equation of the function is:
[tex] f(x) = (1)x + 7 [/tex]
[tex] f(x) = x + 7 [/tex]
The graph of the function, k, is shown in the attachment below.
❌Now, we know that the slope of the function, m, is 1. Therefore, option A is not correct.
We also know that the graph of the function, k, does not pass through the points (-1, -8). We can confirm this looking at the graph. ❌The point (-1, -8) is not on the line of the graph. Therefore, option B is not correct.
❌The zero of k, is the value of x for which the function, f(x) or y = 0. From our graph, y = 0, when x = -7. This can also be referred to as the x-intercept. The zero of k is -7, not 7.
Therefore, option C is not correct.
✅The x-intercept is where the line of the function of intercepts the x-axis. From our graph, the line intercepts the x-axis at x = -7.
So, the x-intercept of the graph of k is -7.
Therefore, option D is the only statement that is TRUE.
Related Questions
6. A graph with a
slope decreases from left to right.
Answers
Answer:
A graph with a slope that decreases from left to right is negative. This slope would mean as x approaches +infinity y would approach -infinity and vice versa. So as x increased y would decrease and as x decreased y would increase. This is called an inverse relationship because the values change in opposite ways.
WILL PAY 40 POINTS AND BRAINLIEST!!!!
A line goes through the points (-3 1) and (-2 4)
(a) What is the slope of the line? Show your work.
(b) Write the equation of the line in point-slope form. Show your work.
(c) Write the equation of the line in slope-intercept form. Show your work.
Answers
Answer:
Part A)
The slope is 3.
Part B)
[tex]\displaystyle y-1=3(x+3)[/tex]
Part C)
[tex]\displaystyle y=3x+10[/tex]
Step-by-step explanation:
We know that the line goes through the points (-3, 1) and (-2, 4).
Part A)
To find the slope of a line given two points, we can use the slope formula:
[tex]\displaystyle m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where (x₁, y₁) and (x₂, y₂) are our two points.
So, let’s let (-3, 1) be (x₁, y₁) and let (-2, 4) be (x₂, y₂). Substitute appropriately:
[tex]\displaystyle m=\frac{4-1}{-2-(-3)}[/tex]
Evaluate:
[tex]\displaystyle m=\frac{3}{-2+3}=\frac{3}{1}=3[/tex]
Hence, the slope of our line is 3.
Part B)
Point-slope form is given by:
[tex]\displaystyle y-y_1=m(x-x_1)[/tex]
Where m is our slope and (x₁, y₁) is a point.
So, let’s substitute 3 for m.
For our point, we can use either of the two given. Let’s use (-3, 1) for consistency. So, let (-3, 1) be (x₁, y₁). Therefore:
[tex]\displaystyle y-1=3(x-(-3))[/tex]
Simplify. Hence, our point-slope form is:
[tex]\displaystyle y-1=3(x+3)[/tex]
Part C)
To rewrite into slope-intercept form, we can just solve for y from our point-slope form. So, we have:
[tex]\displaystyle y-1=3(x+3)[/tex]
Distribute on the right:
[tex]\displaystyle y-1=3x+9[/tex]
Add 1 to boths sides. So, our slope-intercept equation is:
[tex]\displaystyle y=3x+10[/tex]
Determine the intercepts of the line.
x-intercept(_,_)
y-intercept(_,_)
Answers
Answer:
the X - intercept is (-7,0)
the Y - intercept is (0,2)
Step-by-step explanation:
the Y intercept is where the line crosses the Y axis
the X intercept is where the line crosses the X axis
Hope this helps
Which terms are like terms in the following expression? 3x + 3xy – 2x + 5y + 5x2
3x, -2x and 5x2
3x and -2x
3x, 3xy, -2x and 5y
All terms are alike.
Answers
Answer:
3x, -2x
Step-by-step explanation:
they both have x as a variable
Answer:
3x, -2x
Step-by-step explanation:
Find the slope of the line through the pair of points.
(1,15) and (-3,-6)
Answers
Answer:
21/4
Step-by-step explanation:
-6-15/ -3-1= -21/-4=21/4
Solve.
24 + d = 30
d =
Answers
Answer:
I think d = 6 because 24 + 6 = 30
Answer:
d=6
Step-by-step explanation:
HELP PLZ can someone simplify this equation
Answers
7n² + 48n + 42
Combine like terms, -8n x -6n= 48n
-6 x -7= 42
Answer:
-49n^3 -n²+92n+42
Step-by-step explanation:
(7n²-8n-6)(-6n-7)
-42n^3-49n²+48n²+56n+36n+42
-49n^3 -n²+92n+42
What is the equation of the line that passes through the point (−3,4) and has a slope of 1 ?
Answers
Answer:
y = x + 7
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Here m = 1, thus
y = x + c ← is the partial equation
To find c substitute (- 3, 4) into the partial equation
4 = - 3 + c ⇒ c = 4 + 3 = 7
y = x + 7 ← equation of line
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We have following equation to find the point-slope form of the linear functions.
[tex]y - y(0) = m \times ( \: x - x(0) \:) [/tex]
In which :
[tex]y(0) = y \: \: given \: \: point = 4[/tex]
[tex]x(0) = x \: \: given \: \: point = - 3[/tex]
[tex]m = slope = 1[/tex]
Now just need to put the coordinates and the slope in the above equation.
[tex]y - 4 = 1 \times ( \: x - ( - 3) \: )[/tex]
[tex]y - 4 = x + 3[/tex]
Add sides 4
[tex]y - 4 + 4 = x + 3 + 4[/tex]
[tex]y = x + 7[/tex]
Done...
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graph the function h(x) = (x - 5)2+ 6
Answers
Answer:
x = 2
Step-by-step explanation:
have a nice rest of your day
I just need help with the graphing the rest of them are all drop downs lol
Answers
Solve 9(8x + 5) + 7 if x = 0.25.
pls help
Answers
Answer: 70
Multiply 8 by 0.25. Add 5 multiply that by nine then add 7.
Answer:
x= 9/14 or 0.642857
Step-by-step explanation:
Instantaneous vs Average Rate of change
PLEASE AND THANKSSS:))
Answers
what isthe area of the circle or semicircle 2.5
Answers
Answer:
I don't know what your question was but the radius would eqaul .089 so the area is 2.5
Answer:
0.89
Step-by-step explanation:
the area of the. ..............
PLEASE HELP ME I REALLY NEED HELP IN ALGEBRA
(a) Does the graph represent a constant-rate relationship?
(b) Explain how you determined your answer in part A.
(c) If this is a constant-rate relationship, what is the constant rate?
Answers
Answer:
A no it is not
B his is because if you look at 1 on the x axis line you will see it matches 1 on the y axis but if you look at 4 on the x axis it is 2 on the y axis so it is not constant
C Thee was no constant relationship
help please
can you solve this?im times so i need help fast.
Answers
Answer:
C. 1 4 2
Step-by-step explanation:
plz help this is my last try!!!!!!!!!!!!!
Answers
Answer:
4x^6
Step-by-step explanation:
which is the estimate of each product 11/12 x 4/5
Answers
Answer:
[tex]\frac{11}{15}[/tex]
Step-by-step explanation:
[tex]\frac{11}{12} *\frac{4}{5}[/tex]
You can simplify to make life easier
[tex]\frac{11}{3}*\frac{1}{5}=\frac{11}{15}[/tex]
Find the slope of the line that passes through (-3,4) and (-2,-8)
Answers
Answer:
-12
Step-by-step explanation:
The slope formula is y2-y1 divided by x2-x1
I plugged it in and got
-12
I hope this helps :>ex.
What is the measure of angle K?
11°
O 25°
O 50°
O 65°
Answers
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i just took the quiz, it’s 25.
Which expression is equivalent to (2x^2+3x-4)-(x^2-2x+4)
Answers
Answer:
3x + 2 = 14
Step-by-step explanation:
For questions 1 - 2, put the equation in the form ax2+bx+c = 0.
1. (x+2)2 = -X-2
Answers
Answer:
x^2+6x+6=0
Step-by-step explanation:
(x+2)^2=-x-2
(x+2)(x+2)=-x-2
x^2+4x+4=-x-2
+x +2=+x+2
x^2+6x+6=0
how do u all feel about this
Answers
Answer:
BROOOOOO THAT DOPPPEEEE i loveee the colors also its super complex great job
Step-by-step explanation:
·Has to be a number
Answers
Answer:
x=-4
Step-by-step explanation:
PLEASE ANSWER BRAINIEST
Answers
Answer:
first box is 18 second is 32 and third is 8
Step-by-step explanation:
Answer:
Step-by-step explanation:
3 6 8
18 36 48
your ratio is 1:6, so however many boxes you have, just multiply by 6 to get the candle number
2x+y =8 and y=x-7 solve by substitution
Answers
Answer:
you can do this by this please vote also
what is the equation shown on this graph?
Answers
Answer:
y=1
Step-by-step explanation:
there is no slope therefore dont place it. however there is a Y intercept.
A taxi company charges a flat fee of $2.50 plus $0.95 for each mile
traveled.
Which of the following equations correctly represents the total taxi
fare, t, given the number of miles traveled, m?
Answers
Answer:
t=0.95m+2.5
Step-by-step explanation:
Answer:
tm+3.45=?
Step-by-step explanation:
I think
hope this helps
Write an equation of a vertical line that contains the point (-2,5)
Answers
Answer:
x=-2
Step-by-step explanation:
The line is vertical and/or undefined and it passes through the point (-2,5).
PLEASEEEEEEEER HELP ME!!
Answers
Please help!!!!!
Fill in the following table with values, observe the pattern, and write an equation relating the second and fourth columns.
Answers
Answer: Answer from Plato
Step-by-step explanation:
Answer:
For the sin table:
Step-by-step explanation: