Question

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

Answer 1

Step-by-step 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 = (y_2 -y_1 )/(x_2 - x_1)`

Substitute the coordinate points in the formula.

`m = (2 - 0)/(0 - ( - 4)) \\ m = (2)/( 4) \\ m = (1)/(2)`

Therefore, the slope is 2.

Rewrite the equation in slope-intercept.

`y = (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 = (1)/(2) x + b`

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

`2 = (1)/(2) (0) + b \\ 2 = 0 + b \\ 2 = b`

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

Rewrite the equation.

`y = (1)/(2) x + 2`

Answer

`\large \boxed{y = (1)/(2) x + 2}`

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