Question

A line passes through the point (-2,9) and has a slope of "-8" Write an equation in slope-intercept form for this line.

Answer 1

Let's solve this problem step-by-step:

First, let's set up the point-slope form:

 ⇒ $(y-y_1)=m(x-x_1)$

• (x₁,y₁) ==> point on the line
• m      ==> value of slope of the line

Let's examine what we are given:

• (-2,9) ==> point on the line
• -8      ==> slope of the line

Let's plug in all the known values in the point-slope form:

 $(y-9)=-8(x+2)$

To convert from point-slope form to slope-intercept form:

 ⇒ must solve for 'y'

     ⇒ (in other words) must isolate y to one side and everything else to  

         the other side

Let's solve:

 $(y-9)=-8(x+2)\\y-9=-8x-16\\y=-8x-7$

Answer: y= -8x - 7

Hope that helps!

Answer 2

Hi student, let me help you out! :)

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We are asked to find the slope intercept equation for the line that passes through $\pmb{(-2,9)}$ and has a slope of $\pmb{-8}$.

$\triangle~\fbox{\bf{KEY:}}$

• The slope is the number before x (in slope intercept form)

Here's the slope intercept equation:

$\dag~\mathtt{y=mx+b}$ (slope is denoted as "m")

So, substitute -8 for m:

$\dag~\mathtt{y=-8x+b}$

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Now, let's find the y intercept, which is b.

Here's how it's done:

Remember the point that the line contains, (-2,9)?

Well, let's substitute its y-coordinate, 9, for y:

$\dag~\mathtt{9=-8x+b}$

Do the same thing with its x-coordinate, -2, only substitute it for x:

$\dag~\mathtt{9=-8(-2)+b}$

Upon simplifying,

$\dag~\mathtt{9=16+b}$

Solve for b.

$\dag~\mathtt{9-16=b}$

$\dag~\underline{\mathtt{b=-7}}$

Thus, the equation is $\bigstar~\underline{\boxed{\mathrm{y=-8x-7}}}$.

Hope it helps you out! :D

Ask in comments if any queries arise.

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~Just a smiley person helping fellow students :)

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