Sure! Let's start by finding the [tex]$x$[/tex]-intercept and [tex]$y$[/tex]-intercept for the given line with the equation [tex]$-3x + 6y = 12$[/tex].
### Finding the [tex]$y$[/tex]-Intercept
1. To find the [tex]$y$[/tex]-intercept, set [tex]$x$[/tex] to [tex]$0$[/tex] in the given equation and solve for [tex]$y$[/tex].
2. Substituting [tex]$x = 0$[/tex] into the equation [tex]$-3x + 6y = 12$[/tex]:
[tex]\[
-3(0) + 6y = 12
\][/tex]
[tex]\[
6y = 12
\][/tex]
[tex]\[
y = \frac{12}{6} = 2
\][/tex]
3. Therefore, the [tex]$y$[/tex]-intercept is [tex]$(0, 2)$[/tex].
### Finding the [tex]$x$[/tex]-Intercept
1. To find the [tex]$x$[/tex]-intercept, set [tex]$y$[/tex] to [tex]$0$[/tex] in the given equation and solve for [tex]$x$[/tex].
2. Substituting [tex]$y = 0$[/tex] into the equation [tex]$-3x + 6y = 12$[/tex]:
[tex]\[
-3x + 6(0) = 12
\][/tex]
[tex]\[
-3x = 12
\][/tex]
[tex]\[
x = \frac{12}{-3} = -4
\][/tex]
3. Therefore, the [tex]$x$[/tex]-intercept is [tex]$(-4, 0)$[/tex].
### Plotting the Points and Graphing the Line
1. Plot the [tex]$y$[/tex]-intercept [tex]$(0, 2)$[/tex] on the graph. This is the point where the line crosses the [tex]$y$[/tex]-axis.
2. Plot the [tex]$x$[/tex]-intercept [tex]$(-4, 0)$[/tex] on the graph. This is the point where the line crosses the [tex]$x$[/tex]-axis.
3. Use a ruler or a straight edge to draw a line through these two points. This line represents the equation [tex]$-3x + 6y = 12$[/tex].
By following these steps, you now have the [tex]$x$[/tex]-intercept and [tex]$y$[/tex]-intercept and you can accurately graph the line on a coordinate plane.
