Question

A line is graphed below. Write an equation in the form y = mx + b that represents this line

Answer 1

Explanation

• Slope-Intercept form

$y = mx + b \\ m = slope \\ b = y - intercept$

• Calculate the slope with two given coordinate by using rise over run.

$\begin{cases}(x_1,y_1) = ( - 4,0) \\ (x_2,y_2) = ( 0,2) \end{cases}$

These two coordinate points are part of the graph and can be used to find the slope.

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

Substitute the coordinate points in the formula.

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

Therefore, the slope is 2.

Rewrite the equation in slope-intercept.

$y = \frac{1}{2} x + b$

• Calculate the y-intercept by substituting any given points in new rewritten equation.

$(x,y) = ( 0,2)$

I will be substituting these coordinate points in the equation.

$y = \frac{1}{2} x + b$

Substitute x = 0 and y = 5 in the equation.

$2 = \frac{1}{2} (0) + b \\ 2 = 0 + b \\ 2 = b$

Therefore the y-intercept is (0,2).

Rewrite the equation.

$y = \frac{1}{2} x + 2$

Answer

$\large \boxed{y = \frac{1}{2} x + 2}$

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