Question

given (3, -2) and (-2, 3)
a) Write the equation of the line in slope-intercept form that passes
through these two points.
b) What is the slope of any line parallel to this line? Why?
c) What is the slope of any line perpendicular to this line? Why?

Answer 1

Part a: slope intercept form is y=mx+b, you need to find the slope between the points you are given and then plug in a (x,y) point and slope into your equation to find your b value.

Answer 2

Do you need me to do it step by step?

Answer 3

yes please

Answer 4

\[y=mx+b\]
\[m=slope, b=y-intercept\]

Answer 5

To find your slope (m):\[m= \frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }\]

Answer 6

\[m=\frac{ 3-(-2) }{ -2-3 }=-1\]

Answer 7

\[y=-1(x)+b\]

Answer 8

Now, you a point you have to find 'b'

Answer 9

\[-2=-3+b\]
\[b=1\]

Answer 10

So your equation is \[y=-x+1\]

Answer 11

Part b: Parallel lines have the same slopes. Thus any line with a slope of -1 would be parallel to your line.

Answer 12

Part c: Perpendicular lines have slopes that are negative reciprocals. Thus any line with a slope of 1 would be perpendicular to your line.