Question

A line passes through the points (−3,1) and (1,−2). This line can be modeled by the equation y=ax+b. What are the values (in fraction and decimal form) of a and b?

Answer 1

see explanation

Explanation:

y = ax + b is the equation in slope- intercept form

where a is the slope of the line and b is the y- intercept

To find a use the slope formula

a = (y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (- 3, 1) and (x₂, y₂ ) = (1, - 2)

a =
`(-2-1)/(1+3)` = -
`(3)/(4)` = - 0.75, hence

y = - 0.75 + b

To find b substitute either of the 2 points into the equation

using (1, - 2), then

- 2 = - 0.75 + b ⇒ b = - 2 + 0.75 = - 1.25 = - 1
`(1)/(4)`