Question

What is the slope of the line shown in the graph?What is the y value of the y- intercept of the line shown in the graph? what is the equation of line?

Answer 1

slope = -5/4

The y value of y intercept is 5

$\begin{gathered} E\text{quaton of the line:} \\ y\text{ = }\frac{-5}{4}x\text{ + 5} \end{gathered}$

Explanation

To get the slope of the line, we will pick any two points on the line

using points: (0, 5) and (8, -5)

We will apply the slope formula:

$m\text{ = }\frac{y_2-y_1}{x_2-x_1}$$\begin{gathered} x_1=0,y_1=5,x_2=8,y_2\text{ = }-5 \\ In\text{sert into the formula:} \\ m\text{ = }\frac{-5-5}{8-0} \\ m\text{ = }\frac{-10}{8} \end{gathered}$$\begin{gathered} m\text{ = }\frac{-5}{4} \\ \\ \text{Hence, the slope of the line is }\frac{-5}{4} \end{gathered}$

The y-intercept of a line is the value of y when x = 0

We will check the graph for the value of y when x = 0. This is also the point the line crosses the y axis.

The line crosses the y axis at y = 5

At this point, x = 0

Hence, the value of y of the y-intercept of the line shown is 5

The equation of line is given as:

y = mx + b

where m = slope

b = y-intercept

using the format above, our m = slope = -5/4

b = y-intercept = 5

inserting the values into the equation of line, the equation of line becomes:

$y\text{ = }\frac{-5}{4}x\text{ + 5}$