Question

The formula y = mx + b is the slope-intercept form of the equation of a line where m is the slope of the line, b is the y-intercept, and (x,y) is a solution of the equation. The equation solved for b is b = y - mx. True False A у – ь False The equation solved for x is x = A True The equation solved for m is m = x (y – b). True False

Answer 1

The slope-intercept form is

$y=mx+b$

If we solve for b, we have to subtract mx on each side.

$\begin{gathered} y-mx=mx-mx+b \\ b=y-mx \end{gathered}$

Therefore, the first statement is true.

If we solve for x, first, we subtract b on each side.

$\begin{gathered} y-b=mx+b-b \\ y-b=mx \end{gathered}$

Then, we divide the equation by m.

$\begin{gathered} \frac{mx}{m}=\frac{y-b}{m} \\ x=\frac{y-b}{m} \end{gathered}$

Therefore, the second statement is true.

If we solve the equation for m, first, we subtract b on each side.

$\begin{gathered} y-b=mx+b-b \\ y-b=mx \end{gathered}$

Then, we divide by x.

$\begin{gathered} \frac{y-b}{x}=\frac{mx}{x} \\ \frac{y-b}{x}=m \end{gathered}$

Therefore, the third statement is false.