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)` , y- intercept = 5

Explanation:

calculate the slope m using the slope formula

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

with (x₁, y₁ ) = (0,5) and (x₂, y₂ ) = (4, 0) ← 2 points on the line

m =
`(0-5)/(4-0)` =
`(-5)/(4)` = -
`(5)/(4)`

the y- intercept is the value of y on the y- axis where the line crosses, so

y = 5 is the y- intercept

Answer 2

slope = -5/4

The y value of y intercept is 5

`\begin{gathered} E\text{quaton of the line:} \\ y\text{ = }(-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{ = }(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{ = }(-5-5)/(8-0) \\ m\text{ = }(-10)/(8) \end{gathered}`
`\begin{gathered} m\text{ = }(-5)/(4) \\ \\ \text{Hence, the slope of the line is }(-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{ = }(-5)/(4)x\text{ + 5}`