Question

Find the slope(m) and y-intercept (b) of each representation below.

Answer 1

Answer:

m= 15

b= 45

y= 15x +45

Concept:

Overall equation

The equation of a line in slope-intercept form is given by y= mx +b, where m is the slope and b is the y-intercept.

Slope, m

The slope is the measure of how steep the line is. It also defines how the y-axis changes with respect to the x-axis. The formula for finding slope is as shown below.

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

where $(x_1,y_1)$ is the first coordinate and $(x_2,y_2)$ is the second coordinate

y-intercept, b

This is the y-value in which the line cuts through the y-axis (vertical axis).

Working:

Slope, m

Let's identify two pairs of coordinates on the line.

2 square units on the y-axis represent $30. Thus, 1 unit on the y-axis represents $15.

The 2 points are: (0, 45) and (5, 120)

Substitute the 2 points into the slope formula:

Slope

= $\frac{120-45}{5-0}$

= $\frac{75}{5}$

= 15

Thus, m= 15.

y-intercept, b

From the graph, the line cuts through the y-axis at y= 45.

Thus, b= 45.

Overall equation

Substitute m= 15 & b= 45 into y= mx +b:

∴ The equation of the line is y= 15x +45.

Additional:

To learn more about slope-intercept form, do check out: brainly.com/question/26351470