Find the x and y intercept of y=(3/4)x-5
Understand the Problem
The question is asking to find the x and y intercepts of the linear equation y = (3/4)x - 5. The y-intercept is the point where the line crosses the y-axis (where x=0), and the x-intercept is the point where the line crosses the x-axis (where y=0).
Answer
x-intercept: $(\frac{20}{3}, 0)$ y-intercept: $(0, -5)$
Answer for screen readers
x-intercept: $(\frac{20}{3}, 0)$ y-intercept: $(0, -5)$
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 $y$: $y = \frac{3}{4}(0) - 5$ $y = 0 - 5$ $y = -5$ So, the y-intercept is at the point $(0, -5)$.
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Find the x-intercept To find the x-intercept, set $y = 0$ in the equation and solve for $x$: $0 = \frac{3}{4}x - 5$
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Isolate the x term Add 5 to both sides of the equation: $5 = \frac{3}{4}x$
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Solve for x Multiply both sides of the equation by $\frac{4}{3}$ to isolate $x$: $\frac{4}{3} \cdot 5 = \frac{4}{3} \cdot \frac{3}{4}x$ $\frac{20}{3} = x$ So, the x-intercept is at the point $(\frac{20}{3}, 0)$.
x-intercept: $(\frac{20}{3}, 0)$ y-intercept: $(0, -5)$
More Information
The x-intercept is also known as the root of the equation.
Tips
A common mistake is to mix up the x and y values when stating the intercepts. Remember that the y-intercept occurs when $x=0$, and the x-intercept occurs when $y=0$. For example, stating the y-intercept as $(-5, 0)$ is incorrect.
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