Answer:
[tex] y = \frac{3}{4}x - 2 [/tex]
Step-by-step explanation:
Equation of a line is given as [tex] y = mx + b [/tex]
Where,
m = slope of the line = [tex] \frac{y_2 - y_1}{x_2 - x_1} [/tex]
b = y-intercept, which is the value at the point where the line intercepts the y-axis. At this point, x = 0.
Let's find m and b to derive the equation for the line.
[tex] m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
Use the coordinate pair of any two points on the line. Let's use the following,
[tex] (0, -2) = (x_1, y_1) [/tex] => on the line, when x = 0, y = -2
[tex] (4, 1) = (x_2, y_2) [/tex] => on the line, when x = 4, y = 1
Plug in the values and solve for m
[tex] m = \frac{1 - (-2)}{4 - 0} [/tex]
[tex] m = \frac{1 + 2}{4} [/tex]
[tex] m = \frac{3}{4} [/tex]
b = -2 (the line intercepts the y-axis at this point)
Our equation would be =>
[tex] y = mx + b [/tex]
[tex] y = \frac{3}{4}x + (-2) [/tex]
[tex] y = \frac{3}{4}x - 2 [/tex]
