Find the x and y intercepts of the equation y = (1/2)x - 2
Understand the Problem
The question asks us to find the x and y intercepts of the given linear equation y = (1/2)x - 2. To find the y-intercept, we set x = 0 and solve for y. To find the x-intercept, we set y = 0 and solve for x.
Answer
x-intercept: $(4, 0)$ y-intercept: $(0, -2)$
Answer for screen readers
x-intercept: $(4, 0)$ y-intercept: $(0, -2)$
Steps to Solve
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Find the y-intercept To find the y-intercept, set $x = 0$ in the equation and solve for $y$. $$ y = \frac{1}{2}(0) - 2 $$
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Solve for y Simplify the equation. $$ y = 0 - 2 $$ $$ y = -2 $$ Thus, the y-intercept is $(0, -2)$.
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Find the x-intercept To find the x-intercept, set $y = 0$ in the equation and solve for $x$. $$ 0 = \frac{1}{2}x - 2 $$
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Solve for x Add 2 to both sides of the equation. $$ 2 = \frac{1}{2}x $$
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Isolate x Multiply both sides of the equation by 2. $$ 2 * 2 = x $$ $$ 4 = x $$ Thus, the x-intercept is $(4, 0)$.
x-intercept: $(4, 0)$ y-intercept: $(0, -2)$
More Information
The x and y intercepts are the points where the line crosses the x and y axes, respectively. They are useful for graphing the line.
Tips
A common mistake is to mix up the x and y intercepts. Remember that to find the x-intercept, you set $y = 0$, and to find the y-intercept, you set $x = 0$. Also, be careful with the arithmetic when solving for x and y.
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