Find the x-intercept and the y-intercept of the equation 2x + 3y = -6, then use them to graph the line.
Understand the Problem
The problem asks to find the x and y intercepts from the equation of a line, specifically, (2x + 3y = -6). Then, these intercepts should be used to graph the line.
Answer
x-intercept: $-3$ y-intercept: $-2$
Answer for screen readers
x-intercept: -3 y-intercept: -2
Steps to Solve
- Find the x-intercept
To find the x-intercept, set $y = 0$ in the equation and solve for $x$: $$2x + 3(0) = -6$$ $$2x = -6$$ $$x = -3$$ The x-intercept is $-3$.
- Find the y-intercept
To find the y-intercept, set $x = 0$ in the equation and solve for $y$: $$2(0) + 3y = -6$$ $$3y = -6$$ $$y = -2$$ The y-intercept is $-2$.
- Use the intercepts to plot the line
Plot the x-intercept at the point $(-3, 0)$ and the y-intercept at the point $(0, -2)$. Draw a straight line through these two points.
x-intercept: -3 y-intercept: -2
More Information
The x and y intercepts are points where the line crosses the x and y axes respectively.
Tips
A common mistake is swapping the values of $x$ and $y$ when calculating the intercepts. Remember to set $y=0$ to find the x-intercept and $x=0$ to find the y-intercept.
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