Find the x-intercept and the y-intercept of the equation 4x - 6y = 12. Then use them to graph the line.
Understand the Problem
The question asks to find the (x)-intercept and (y)-intercept of the line given by the equation (4x - 6y = 12). Then asks to graph the line using these intercepts.
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 $x$.
$4x - 6(0) = 12$ $4x = 12$ $x = \frac{12}{4}$ $x = 3$
Therefore, the $x$-intercept is 3.
- Find the y-intercept To find the $y$-intercept, set $x = 0$ in the equation and solve for $y$.
$4(0) - 6y = 12$ $-6y = 12$ $y = \frac{12}{-6}$ $y = -2$
Therefore, the $y$-intercept is -2.
- Plot the intercepts and graph the line Plot the points $(3, 0)$ and $(0, -2)$ on the coordinate plane. Draw a straight line through these two points. This line represents the graph of the equation $4x - 6y = 12$.
x-intercept: $3$ y-intercept: $-2$
More Information
The x-intercept is the point where the line crosses the x-axis, and the y-intercept is the point where the line crosses the y-axis. These points are useful for graphing linear equations quickly.
Tips
A common mistake is to mix up the x and y values when calculating intercepts. For example, some students might mistakenly set $x=0$ when trying to find the $x$-intercept or vice versa. Always remember to set $y=0$ to find the $x$-intercept and $x=0$ to find the $y$-intercept. Another common mistake is making arithmetic errors when solving for $x$ and $y$. Be careful with signs and division.
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