Write the slope-intercept equation of the line passing through (4,6) and (0,-8).

Answer:​

Answer:

[tex]y=\frac{7}{2} x -8[/tex]

Step-by-step explanation:

We are given that a line contains these 2 points: (4,6) and (0,-8), in slope-intercept form

Slope-intercept form is given as y=mx+b, where m is the slope and b is the value of y at the y intercept

First, we need to find the slope of the line

The slope can be calculated using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

Even though we have 2 points, let's label their values to avoid any confusion and mistakes when calculating:

[tex]x_1=4\\y_1=6\\x_2=0\\y_2=-8[/tex]

Now substitute into the formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{-8-6}{0-4}[/tex]

Subtract

m=[tex]\frac{-14}{-4}[/tex]

Divide

m=[tex]\frac{7}{2}[/tex]

The slope is 7/2

Here is the equation of the line so far:

[tex]y=\frac{7}{2}x + b[/tex]

We now need to find b

As the equation passes through (4,6) and (0,-8), we can use either one of them to help solve for b.

Taking (4,6) for instance:

[tex]6=\frac{7}{2}(4) + b[/tex]

Multiply

[tex]6=14 + b[/tex]

Subtract

-8 = b

The equation therefore is:

[tex]y=\frac{7}{2} x -8[/tex]

Topic: slope-intercept form

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