Question

What is the equation of the line that passes
through the points (2,-3) and (3, 1)?

Answer 1

-3 - 4*2 + 1 is the slope-intercept equation

1 = 12 - 2 is the slope-intercept equation

point-slope equation is -3 - 1 = 4 ( 2 - 3)

Explanation:

Slope-intercept formula:

y = mx + b

First we have to find the slope,

(1). 3 - 2 / 1 + 3 = 1/4

(2). 1 is x and 4 is y

(3). x/y is slope. so,

4/1 = 4

so the slope is 4!

Now back to the formula,

y = mx + b --> -3 = 4*2 + 1 --> -3 = 8 + 1

So -3 = 8 + 1 is the slope-intercept equation for equation 1.

Equation 2:

y = mx + b --> 1 = 4*3 - 2 --> 1 = 12 - 2

So 1 = 12 - 2 is the slope-intercept equation for equation 2

Point-Slope Formula:

y₁ - y₂ = m ( x₁ - x₂)

Substitution,

-3 - 1 = 4 ( 2 - 3)

So the point-slope equation is -3 - 1 = 4 ( 2 - 3)

Hope this helps! I spent a lot of time on this one question :)

Answer 2

Y=4x+11 because the y intercept is 11 and the slope is 4