Find the x-intercept and y-intercept of the equation y = (4/3)x - 5.
Understand the Problem
The question requires finding the x-intercept and y-intercept of the given linear equation. 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: 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 $x$: $$2x + 3(0) = 6$$
- Solve for x
Simplify the equation: $$2x = 6$$ Divide both sides by 2: $$x = \frac{6}{2} = 3$$ So, the x-intercept is 3.
- Find the y-intercept
To find the y-intercept, set $x = 0$ in the equation and solve for $y$: $$2(0) + 3y = 6$$
- Solve for y
Simplify the equation: $$3y = 6$$ Divide both sides by 3: $$y = \frac{6}{3} = 2$$ So, the y-intercept is 2.
x-intercept: 3 y-intercept: 2
More Information
The x-intercept is the point where the line crosses the x-axis, which occurs when $y = 0$. The y-intercept is the point where the line crosses the y-axis, which occurs when $x = 0$.
Tips
A common mistake is to mix up the x and y values when calculating the intercepts, or incorrectly solving for x and y e.g. to divide instead of multiply or forget to divide to isolate the variable.
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