Question

The graph above is of the linear function y = mx + b. Which of the following could represent the graph of y = cmx + b, where c is a positive number greater than 1?

Answer 1

The general form of an equation of a line is;

y = mx + b

You can obtain the equation of the given line by calculating the slope m and the y-intercept.

You use the following formula for the slope:

$m=\frac{y_2-y_1}{x_2-x_1_{}}$

where (x1,y1) and (x2,y2) are two points of the line. You can observe that two pointsof the line are (0,-2) and (4,0).

You replace the previous coordinates into the formula for m:

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

Next, you use the same formula for m to obtain the y-intercep b. You proceed as follow:

$m=\frac{y-y_1}{x-x_1}$

where (x1,y1) is a point of the line, if you use the point (0,-2), you have:

$\begin{gathered} m=\frac{y-(-2)}{x-0}=\frac{y+2}{x} \\ mx=y+2 \\ y=mx-2 \\ y=\frac{1}{3}x-2 \end{gathered}$

Hence, the equation of the line of the graph is:

y = 1/3x - 2