Question

5. Write equations in slope-intercept form for three different lines that intersect at (–2, 3). Show your work.

Answer 1

Answer:

Equations in slope-intercept form for three different lines that intersect at (–2, 3) are y=-x+1  ,  y=3  and y=x+5

Step-by-step explanation:

General equation of slope intercept form : $y-y_1=m(x-x_1)$

We are supposed to find equations in slope-intercept form for three different lines that intersect at (–2, 3).

$(x_1,y_1)=(-2,3)$

Substitute the value in the general equation

y-3=m(x+2)

Now substitute any 3 values of m

At m = -1

$\Rightarrow y-3=-x-2 \\\Rightarrow y=-x+1$

At m =0

$\Rightarrow y-3=0 \\\Rightarrow y=3$

At m =1

$\Rightarrow y-3=x+2 \\\Rightarrow y=x+5$

They all intersect at the given point.

So, equations in slope-intercept form for three different lines that intersect at (–2, 3) are y=-x+1  ,  y=3  and y=x+5