Question

This exercise emphasizes the "mechanical aspects" of working with linear equations. Find the equation of a line with the following characteristics.

(a) Passing through the points (1, −1) and (−3, 4).

please show your work and explanation. I am having a hard time with doing the problem step by step! Thank you.

Answer 1

if I have two points on a straight line, I can always find the slope; that's what the slope formula is y=mx+c

m=change in y/change in x

->m=(y2-y1)/(x2-x1)

The given two points are (1,-1)(-3,4)

m=(4-(-1))/(-3-1)

m=-5/4

so here y=(-5/4)x+c

Using the point (1, -1), I get:

y=(-5/4)x+c

-1=(-5/4)(1)+c

c=-1+(5/4)

c=(-4+5)/4

c=1/4

there fore y=(-5/4)x+1/4

Using the point (-3,4), I get:

y=(-5/4)x+c

4=(-5/4)(-3)+c

4=15/4+c

c=4-(15/4)

c=(16-15)/4

c=1/4

there fore y=(-5/4)x+1/4

so finally we conclude y=(-5/4)x+1/4