Question

Mario compared the slope of the function graphed below to the slope of the linear function that has an x-intercept of 1 and a y-intercept of -2.
Find the slope of both lines. In the answer box give the slope of the steeper line.

Answer 1

Answer:

The linear equation in the slope-intercept form will be:

$y\:=\:\frac{2}{3}x+64$

Step-by-step explanation:

From the line graph, taking two points

• (21, 78)

• (27, 82)

Finding the slope between (21, 78) and (27, 82)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(21,\:78\right),\:\left(x_2,\:y_2\right)=\left(27,\:82\right)$

$m=\frac{82-78}{27-21}$

$m=\frac{2}{3}$

We know that the slope-intercept of the line equation is

$y = mx+b$

where m is the slope and b is the y-intercept

substituting (21, 78) and m = 2/3 in the slope-intercept of the line

$y = mx+b$

$78=\frac{2}{3}\left(21\right)+b$

switch sides

$\frac{2}{3}\left(21\right)+b=78$

$14+b=78$

$b=64$

substituting b = 64 and m = 2/3 in the slope-intercept of the line

$y = mx+b$

$y\:=\:\frac{2}{3}x+64$

Therefore, the linear equation in the slope-intercept form will be:

$y\:=\:\frac{2}{3}x+64$