Question

If a line passes through the points (-5,-4) and (3,-1), the equation of the line is?

Answer 1

answer: y = 1.5x - 5.5

explanation:

use y = mx +b to model your equation

(m = slope, b = y-intercept)

let's start by finding slope

to find slope, subtract the y values over the x values.

- 4 - (-1) / - 5 - (-3)

solve and simplify.

 -3 / -2

two negatives equals a positive, so convert into a decimal and remove the negative

you get 1.5.

now, plug the slope a y and x value into the equation to find b, the missing value.

-1 = 1.5(3) + b

-1 = 4.5 + b

-5.5= b

so, your equation is y = 1.5x - 5.5.

Answer 2

y = $\frac{3}{8}$ x - $\frac{17}{8}$

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- 5, - 4 ) and (x₂, y₂ ) = (3 , - 1 )

m = $\frac{-1+4}{3+5}$ = $\frac{3}{8}$

the partial equation is y = $\frac{3}{8}$ x + c

to find c substitute either of the 2 points into the partial equation

using (3, - 1 ), then

- 1 = $\frac{9}{8}$ + c ⇒ c = - $\frac{17}{8}$

y = $\frac{3}{8}$ x - $\frac{17}{8}$ ← in slope-intercept form