Question

Write the equation of a line that

passes through the following points
:
Point 2: (0,-8)
Point 1: (-3,0)

Answer 1

`y = (-8)/(3)x - 8`

Explanation:

Solving for the equation of the line with two points:

Let's remind ourself of the slope - intercept formula:
`y = mx + b`

We first have to find the slope of the line. This is found by using the formula :

`(y_1 - y_2)/(x_1 - x_2)`

We have to find the change in y (Δy) and divide it by the change in x (Δx)

We then have to plug in a coordinate given to us, and use the point's x and y value to find the y - intercept

Step 1: Slope

Let's use the slope formula

`(0 - (-8))/(-3 - 0) = (8)/(-3)`

Slope = -8/3

Step 2: Y - Intercept

To find the y - intercept, we'll update our slope - intercept formula with the slope, and plugin a point. Let's use (-3,0)

`y = (-8)/(3)x + b`

`0 = (-8)/(3)(-3) + b`

`0 = (24)/(3) + b`

`0 = 8 + b`

`b = -8`

Step 3: Equation

Let's input our slope and y - intercept to the equation
`y = mx + b`

Slope = -8/3

Y - Intercept = -8

Equation:
`y = (-8)/(3)x - 8`

-Chetan K