Find the x-intercept and the y-intercept of 4x - 6y = 12. Then use them to graph the line.
Understand the Problem
The question asks us to find the x and y intercepts of the equation 4x - 6y = 12, and then use the intercepts to graph the line.
Answer
x-intercept: 3 y-intercept: -2
Answer for screen readers
x-intercept: 3 y-intercept: -2
Steps to Solve
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Find the x-intercept To find the x-intercept, set $y = 0$ in the equation and solve for $x$: $$4x - 6(0) = 12$$ $$4x = 12$$ $$x = \frac{12}{4}$$ $$x = 3$$ So, the x-intercept is 3.
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Find the y-intercept To find the y-intercept, set $x = 0$ in the equation and solve for $y$: $$4(0) - 6y = 12$$ $$-6y = 12$$ $$y = \frac{12}{-6}$$ $$y = -2$$ So, the y-intercept is -2.
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Graph the line Plot the x-intercept (3, 0) and the y-intercept (0, -2) on the graph. Draw a straight line passing through these two points.
x-intercept: 3 y-intercept: -2
More Information
The x and y intercepts provide two points that define the given line. Using these two points we can plot the graph of the equation.
Tips
A common mistake is solving for $x$ when finding the $y$-intercept (and vice versa). Remember that to find the $x$-intercept, you must set $y=0$, and to find the $y$-intercept, you must set $x=0$. Another common mistake is incorrectly dividing or simplifying when solving for $x$ or $y$.
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