Question

What is the equation of the line that passes through (0,-3) and (2, 2)?

Answer 1

`y = (5)/(2)x -3`

Explanation:

Given points (0,-3) (2, 2), we can start by solving for the slope of the line by using the formula:

`m = (y2 - y1)/(x2 - x1)`

Let (x1, y1) = (0,-3)

(x2, y2) = (2, 2)

Plug in these values into the slope formula:

`m = (y2 - y1)/(x2 - x1) = (2 - (-3))/(2 - 0) = (5)/(2)`

Therfore, the slope of the line is
`(5)/(2)`.

Next, we must determine the y-intercept of the line. By definition, the y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0.

Using the slope (m) =
`(5)/(2)` and one of the given points, (2, 2), plug in these values into the slope-intercept form, y = mx + b:

y = mx + b

`y = (5)/(2)x + b`

`2 = (5)/(2)(2) + b`

2 = 5 + b

Subtract 5 on both sides of the equation to solve for b:

2 - 5 = 5 + b - 5

-3 = b

The y-intercept (b) = -3.

Therefore, the equation of the line that passes through (0,-3) and (2, 2) is:

`y = (5)/(2)x -3`.