Question

1. What is the x intercept of the graph y=x-32. What is the y intercept of the graph y=x-33. What is the x intercept of the graph y=4x+24. What is the y intercept of the graph y=4x+2

Answer 1

1. The x-intercept of a function is the point where the line crosses the x-axis. At this point, the y-coordinate is equal to zero.

You can identify the point from the graph or calculate the coordinates by replacing the equation of the linear function with y=0 and determine the corresponding value of x.

-Looking at the graph, the red line, that corresponds to the equation y=x-3, crosses the x-axis at point (3,0)

-Replacing the equation of the function by y=0:

`\begin{gathered} y=x-3 \\ 0=x-3 \\ 0+3=x-3+3 \\ 3=x \end{gathered}`

The x-intercept has coordinates at (3,0)

2. The y-coordinate is the point where the red line crosses the y-axis. At this point, the x-coordinate is equal to zero.

You can identify this point directly from the graph, or calculate it by replacing the equation of the line with x=0 and calculate the corresponding value of y.

-Looking at the graph, the red line crosses the y-axis at the point (0,-3)

-Replace the equation with x=0

`\begin{gathered} y=x-3 \\ y=0-3 \\ y=-3 \end{gathered}`

The y-intercept is (0,-3)

3. The equation y=4x+2 is represented in the graph by the blue line

As before, you have to identify the point where the line crosses the x-axis.

-From the graph:

-Replace the equation with y=0 and calculate the corresponding value of x:

`\begin{gathered} y=4x+2 \\ 0=4x+2 \\ 0-2=4x+2-2 \\ -2=4x \\ -(2)/(4)=(4x)/(4) \\ -(1)/(2)=x \end{gathered}`

The x-intercept is (-1/2,0)

4. The y-intercept is the point where the blue line crosses the y-axis.

-You can identify it from the graph:

-Or replace the equation with x=0 and determine the corresponding value of y

`\begin{gathered} y=4x+2 \\ y=4\cdot0+2 \\ y=2 \end{gathered}`

The coordinates of the y-intercept are (0,2)