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.

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]

which of the following equations would model a population with a initial size of 625 that is growing at an annual rate of 8.5%
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3. P=1.085^t+625
4. 8.5t^2+625

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-Factored Form
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URGENTTTTTTT
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(e) 5041 - v + 2r2)
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Check

Your Understanding

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Flag this Question
Question 22 pts
Write an equation for the line that passes through the point (4, -1) and is parallel to the line y = 2x - 5.

Group of answer choices

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Question 32 pts
Write an equation for the line that passes through the point (-2, -4) and is perpendicular to the line y = 3x - 2.

Group of answer choices

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LaTeX: y-4=\frac{1}{3}\left(x-2\right)y − 4 = 1 3 ( x − 2 )


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Question 42 pts
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Group of answer choices

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LaTeX: y-5=2\left(x+1\right)y − 5 = 2 ( x + 1 )


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Question 52 pts
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GUYS PLEASE HELP ME ive been struggling with this for the past 15 minutes

I will pick the brainiest answer!!! Thanks! :)

Graph this line using the slope and y-intercept:
y = 8x - 6
Click to select points on the graph.
8
6
4
No
-6
-4
-2
-10
-8
0
co
4
2
6
10
-2
-4
-6
CO
-104

A group of students was asked, "How many hours did you watch television last week?" Here are their responses: 9, 16, 11, 19, 4, 10, 15, 19