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?

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?

anonymous · Answer

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.

anonymous · Answer

Do you need me to do it step by step?

anonymous · Answer

yes please

anonymous · Answer

$$y=mx+b$$
$$m=slope, b=y-intercept$$

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

$$y=-1(x)+b$$

anonymous · Answer

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

anonymous · Answer

$$-2=-3+b$$
$$b=1$$

anonymous · Answer

So your equation is $$y=-x+1$$

anonymous · Answer

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

anonymous · Answer

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