Question

y = -2x + 5a. What is the slope? b. What is the vertical intercept? c. What is the horizontal intercept? d. Graph the equation

Answer 1

Given: The equation below

`y=-2x+5`

To Determine: The slope, the vertical and horizontal intercept, and the graph of the equation

Solution

The general slope-intercept form of a straight line is as shown below

`\begin{gathered} y=mx+c \\ Where \\ m=slope \\ c=vertical-intercept \end{gathered}`

Let us compare the general slope-intercept form of a straight line to the given

`\begin{gathered} y=mx+c \\ y=-2x+5 \\ slope=m=-2 \end{gathered}`

The vertical intercept is the point where the x values is zero

`\begin{gathered} y=-2x+5 \\ x=0 \\ y=-2(0)+5 \\ y=0+5 \\ y=5 \end{gathered}`

The vertical intercept is y = 5, with coordinate (0, 5)

The horizontal intercept is the point where the y value is zero

`\begin{gathered} y=-2x+5 \\ y=0 \\ 0=-2x+5 \\ 2x=5 \\ x=(5)/(2) \end{gathered}`

The horizontal intercept is x = 5/2, with coordinate (5/2, 0)

The graph of the equation is as shown below

Answer Summary

(a) slope = -2

(b) Vertical intercept, y = 5

(c) Horizontal intercept, x = 5/2