Answer:
(-18,0) x-intercept
(0,-6) y-intercept
Step-by-step explanation:
We are given this is a line.
Slope-intercept form of a line is y=mx+b where m is slope and b is y-intercept.
To find the slope we will need to compute [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 on your line.
The way I like to do this is line up the points vertically and subtract then put 2nd difference over 1st difference.
Like so:
(-15 , -1)
-(-9 , -3)
-------------
-6 2
So the slope is 2/-6 or -1/3.
The equation we have so far without knowing the y-intercept,b, is
y=(-1/3)x+b
Now to find b use one of the points on your line. You get to chose this.
How about (-3,-5)? Sure that's fine.
If (x,y)=(-3,-5) then we have -5=(-1/3)(-3)+b.
Let's solve this for b.
-5=(-1/3)(-3)+b
-5=1+b
Subtract 1 on both sides:
-5-1=b
-6=b
The equation is y=(-1/3)x+-6 or y=(-1/3)x-6.
So b represented the y-intercept so the y-intercept is -6 or (0,-6).
To find the x-intercept, you set y=0 and solve for x:
y=(-1/3)x-6
0=(-1/3)x-6
Add 6 on both sides:
6=(-1/3)x
Multiply both sides by -3:
-18=x
The x-intercept is (-18,0).
