Answer:
[tex]y = \frac{5}{2}x -3[/tex]
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:
[tex]m = \frac{y2 - y1}{x2 - x1}[/tex]
Let (x1, y1) = (0,-3)
(x2, y2) = (2, 2)
Plug in these values into the slope formula:
[tex]m = \frac{y2 - y1}{x2 - x1} = \frac{2 - (-3)}{2 - 0} = \frac{5}{2}[/tex]
Therfore, the slope of the line is [tex]\frac{5}{2}[/tex].
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) = [tex]\frac{5}{2}[/tex] and one of the given points, (2, 2), plug in these values into the slope-intercept form, y = mx + b:
y = mx + b
[tex]y = \frac{5}{2}x + b[/tex]
[tex]2 = \frac{5}{2}(2) + b[/tex]
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:
[tex]y = \frac{5}{2}x -3[/tex].
