Write all linear equations in slope-intercept form.
-With 23.5% commitment, a company can clean up 40% of an energy leak. With 28.5% commitment, it can clean up 80% of an energy leak. Find a linear equation that models the percent cleanup for x percent commitment.
A) $y = x + 40$
B) $y = 8 x + 148$
C) $y = 5 x + 40$
D) $y = 8 x - 148$

Question

Write all linear equations in slope-intercept form.
-With 23.5% commitment, a company can clean up 40% of an energy leak. With 28.5% commitment, it can clean up 80% of an energy leak. Find a linear equation that models the percent cleanup for x percent commitment. 
A) $y = x + 40$
B) $y = 8 x + 148$
C) $y = 5 x + 40$
D) $y = 8 x - 148$

Quizplus · Accepted Answer

The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. To find the slope ($m$), we use the formula $\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Here, the points are (23.5, 40) and (28.5, 80), representing percent commitment and percent cleanup, respectively. Calculating the slope: $m = \frac{80 - 40}{28.5 - 23.5} = \frac{40}{5} = 8$.To find the y-intercept ($b$), we can use one of the points and the slope in the equation $y = mx + b$. Using the point (23.5, 40):$40 = 8(23.5) + b$Solving for $b$, we get:$b = 40 - 8(23.5) = 40 - 188 = -148$.Thus, the equation is $y = 8x - 148$.

Write All Linear Equations in Slope-Intercept Form y=x+40y = x + 40y=x+40

Write All Linear Equations in Slope-Intercept Form $y = x + 40$