Absolutely, let's use intercepts to graph the linear equation [tex]\( -2x + 4y = 16 \)[/tex].
### Steps to Find the Intercepts
1. Finding the x-intercept:
- To find the x-intercept, set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ -2x + 4(0) = 16 \][/tex]
[tex]\[ -2x = 16 \][/tex]
[tex]\[ x = -8 \][/tex]
- So, the x-intercept is at [tex]\( (-8, 0) \)[/tex].
2. Finding the y-intercept:
- To find the y-intercept, set [tex]\( x = 0 \)[/tex] and solve for [tex]\( y \)[/tex]:
[tex]\[ -2(0) + 4y = 16 \][/tex]
[tex]\[ 4y = 16 \][/tex]
[tex]\[ y = 4 \][/tex]
- So, the y-intercept is at [tex]\( (0, 4) \)[/tex].
### Plotting the Intercepts and Graphing the Line
3. Plot the intercepts:
- Begin by drawing the Cartesian coordinate plane.
- Plot the x-intercept [tex]\( (-8, 0) \)[/tex] on the x-axis.
- Plot the y-intercept [tex]\( (0, 4) \)[/tex] on the y-axis.
4. Draw the line:
- Use a ruler to draw a straight line through the points [tex]\( (-8, 0) \)[/tex] and [tex]\( (0, 4) \)[/tex].
- Extend the line in both directions, as it represents all solutions to the equation [tex]\( -2x + 4y = 16 \)[/tex].
### Labeling Intercepts
5. Label the plotted points:
- Clearly mark and label the x-intercept [tex]\( (-8, 0) \)[/tex].
- Clearly mark and label the y-intercept [tex]\( (0, 4) \)[/tex].
By following these steps, you can accurately graph the linear equation [tex]\( -2x + 4y = 16 \)[/tex] using its intercepts. The graph should show a straight line passing through [tex]\( (-8, 0) \)[/tex] and [tex]\( (0, 4) \)[/tex].
### Summary
- x-intercept: [tex]\( (-8, 0) \)[/tex]
- y-intercept: [tex]\( (0, 4) \)[/tex]
- Draw the line passing through these points carefully to represent the equation [tex]\( -2x + 4y = 16 \)[/tex].
