Question

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

Answer 1

y-3=-x-2

y=-x+1

y-3=0

y=3

y-3=x+2

y=x+5

Step-by-step explanation

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Answer 2

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

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