Linear equations

Question

Having trouble understanding the process:

A line passes through (-5,-1) and (-4,-4), write an equation of the line in: a) Slope-Intercept Form, and b) Standard Form

Answer 1

Slope Intercept form:

Slope = Change in y

Change in x

​Points are (-5,-1) and (-4,-4)

Slope = (-4-(-1)) = -3 = -3

(-4-(-5)) 1

General slope-intercept equation y=mx+b, the slope is given by m and the y-intercept is given by b.

Therefore, y=(-3x)+b (Equation 1)

Substituting points (-5,-1) and (-4,-4) in Equation 1 separately gives the same value for b in both the cases, which is -16.

Therefore, y=(-3x)-16

Standard form:

Equation of a line passing through given two points is:

y-y₁ x-x₁

=

y₂-y₁ x₂-x₁

Let point (-5,-1) be designated for coefficient 1 and point (-4,-4) be designated for cofficient 2.

y-(-1) x-(-5)

=

(-4-(-1)) (-4-(-5))

y+1 x+5

=

-3 1

y=(-3x)-16