Sure! Let's graph the line [tex]\( -x + 3y = 6 \)[/tex] by finding the x-intercept and y-intercept.
1. Finding the x-intercept:
To find the x-intercept, set [tex]\( y = 0 \)[/tex] in the equation and solve for [tex]\( x \)[/tex].
[tex]\[
-x + 3(0) = 6 \implies -x = 6 \implies x = -6
\][/tex]
So the x-intercept is [tex]\( (-6, 0) \)[/tex].
2. Finding the y-intercept:
To find the y-intercept, set [tex]\( x = 0 \)[/tex] in the equation and solve for [tex]\( y \)[/tex].
[tex]\[
-(0) + 3y = 6 \implies 3y = 6 \implies y = 2
\][/tex]
So the y-intercept is [tex]\( (0, 2) \)[/tex].
3. Plotting the intercepts on the graph:
- Plot the x-intercept [tex]\((-6, 0)\)[/tex]. This is the point where the line crosses the x-axis.
- Plot the y-intercept [tex]\((0, 2)\)[/tex]. This is the point where the line crosses the y-axis.
4. Drawing the line:
- Once you have plotted both intercepts, draw a straight line through the points [tex]\((-6, 0)\)[/tex] and [tex]\((0, 2)\)[/tex].
By following these steps, you will have successfully graphed the line [tex]\( -x + 3y = 6 \)[/tex].
