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Question

Determine the equation of the line that passes through the points (2, 4) and (-3, 14). Write it in slope-intercept form.

Answer 1

NOTE that using the other point provides an excellent check on your work:

y = mx + b

14 = -2 * (-3)+ b

Simplifying:

14 = 6 + b

Subtracting 6 from both sides of the above equation:

b = 8

and that verifies our previous results.

Answer 2

Two points are given, use two-point form

(y - 2) / (x - 2) = (14 - 4) / (-3 -2)

Answer 3

(2,4), (-3,14) have a line through them with slope = "rise over run" = (14-4)/(-3-2) = 10/-5 =-2

-2 = (y-4)/(x-2)

y-4 = -2(x-2) in slope point form

y-4 = -2x +4

y = -2x +8 in slope intercept form, with y intercept = 8

Answer 4

y=mx+b is the slope-intercept form.

m is the slope that can be found by (y₂-y₁) / (x₂-x₁)

(14-4) / (-3-2)= 10 / (-5)= -2

y=-2x+b

in order to find b, let's use one of the given ordered pairs. (2,4) means that x=2 and y=4, let's pug them in.

4=-2(2) + b

4=-4+b

b= 8

so, the equations should be y=-2x + 8