Respuesta :
Let's solve this problem step-by-step:
First, let's set up the point-slope form:
⇒ [tex](y-y_1)=m(x-x_1)[/tex]
- (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:
[tex](y-9)=-8(x+2)[/tex]
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:
[tex](y-9)=-8(x+2)\\y-9=-8x-16\\y=-8x-7[/tex]
Answer: y= -8x - 7
Hope that helps!
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 [tex]\pmb{(-2,9)}[/tex] and has a slope of [tex]\pmb{-8}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
- The slope is the number before x (in slope intercept form)
Here's the slope intercept equation:
[tex]\dag~\mathtt{y=mx+b}[/tex] (slope is denoted as "m")
So, substitute -8 for m:
[tex]\dag~\mathtt{y=-8x+b}[/tex]
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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:
[tex]\dag~\mathtt{9=-8x+b}[/tex]
Do the same thing with its x-coordinate, -2, only substitute it for x:
[tex]\dag~\mathtt{9=-8(-2)+b}[/tex]
Upon simplifying,
[tex]\dag~\mathtt{9=16+b}[/tex]
Solve for b.
[tex]\dag~\mathtt{9-16=b}[/tex]
[tex]\dag~\underline{\mathtt{b=-7}}[/tex]
Thus, the equation is [tex]\bigstar~\underline{\boxed{\mathrm{y=-8x-7}}}[/tex].
Hope it helps you out! :D
Ask in comments if any queries arise.
#StudyWithBrainly
~Just a smiley person helping fellow students :)
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