Question

Please help! Find the equation of the line (graph provided in attached picture) Use exact numbers. y =_ x+_ ( _ represent blanks in the equation)

Answer 1

Answer:

$y = \frac{3}{4}x - 2$

Step-by-step explanation:

Equation of a line is given as $y = mx + b$

Where,

m = slope of the line = $\frac{y_2 - y_1}{x_2 - x_1}$

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.

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Use the coordinate pair of any two points on the line. Let's use the following,

$(0, -2) = (x_1, y_1)$ => on the line, when x = 0, y = -2

$(4, 1) = (x_2, y_2)$ => on the line, when x = 4, y = 1

Plug in the values and solve for m

$m = \frac{1 - (-2)}{4 - 0}$

$m = \frac{1 + 2}{4}$

$m = \frac{3}{4}$

b = -2 (the line intercepts the y-axis at this point)

Our equation would be =>

$y = mx + b$

$y = \frac{3}{4}x + (-2)$

$y = \frac{3}{4}x - 2$