Find the x-intercept and the y-intercept. Then use them to graph the line, given the equation of a line is: -11x + 4y = -22
Understand the Problem
The question asks to find the x and y intercepts of the line given by the equation $-11x + 4y = -22$, and then to graph the line using these intercepts. To find the x-intercept, we set y = 0 and solve for x. To find the y-intercept, we set x = 0 and solve for y.
Answer
x-intercept: $2$ y-intercept: $-5.5$
Answer for screen readers
x-intercept: $2$ y-intercept: $-5.5$
Steps to Solve
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Find the x-intercept Set $y = 0$ in the equation $-11x + 4y = -22$ and solve for $x$. $-11x + 4(0) = -22$ $-11x = -22$ $x = \frac{-22}{-11}$ $x = 2$
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State the x-intercept The x-intercept is $2$. This means the line crosses the x-axis at the point $(2, 0)$.
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Find the y-intercept Set $x = 0$ in the equation $-11x + 4y = -22$ and solve for $y$. $-11(0) + 4y = -22$ $4y = -22$ $y = \frac{-22}{4}$ $y = -\frac{11}{2}$ $y = -5.5$
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State the y-intercept The y-intercept is $-5.5$. This means the line crosses the y-axis at the point $(0, -5.5)$.
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Graph the line Plot the points $(2, 0)$ and $(0, -5.5)$ on the coordinate plane. Draw a straight line through these two points.
x-intercept: $2$ y-intercept: $-5.5$
More Information
The x and y-intercepts are the points where the line crosses the x and y axes, respectively. The x-intercept always has a y-coordinate of 0, and the y-intercept always has an x-coordinate of 0.
Tips
A common mistake is to mix up the x and y values when calculating the intercepts. Remember that to find the x-intercept, you set $y = 0$, and to find the y-intercept, you set $x = 0$. Another common mistake is to make arithmetic errors when solving for x and y.
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