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:
[tex]\begin{gathered} y=x-3 \\ 0=x-3 \\ 0+3=x-3+3 \\ 3=x \end{gathered}[/tex]
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
[tex]\begin{gathered} y=x-3 \\ y=0-3 \\ y=-3 \end{gathered}[/tex]
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:
[tex]\begin{gathered} y=4x+2 \\ 0=4x+2 \\ 0-2=4x+2-2 \\ -2=4x \\ -\frac{2}{4}=\frac{4x}{4} \\ -\frac{1}{2}=x \end{gathered}[/tex]
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
[tex]\begin{gathered} y=4x+2 \\ y=4\cdot0+2 \\ y=2 \end{gathered}[/tex]
The coordinates of the y-intercept are (0,2)
