Question

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

Answer 1

Answer:

$y = \frac{5}{2}x -3$

Step-by-step explanation:

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

$m = \frac{y2 - y1}{x2 - x1}$

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

(x2, y2) = (2, 2)

Plug in these values into the slope formula:

$m = \frac{y2 - y1}{x2 - x1} = \frac{2 - (-3)}{2 - 0} = \frac{5}{2}$

Therfore, the slope of the line is $\frac{5}{2}$.

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) =  $\frac{5}{2}$ and one of the given points, (2, 2), plug in these values into the  slope-intercept form, y = mx + b:

y = mx + b

$y = \frac{5}{2}x + b$

$2 = \frac{5}{2}(2) + b$

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:

$y = \frac{5}{2}x -3$.