Find the x-intercept and y-intercept of the equation -2(x-1)y-6 = -2x + 2y = -2x+8
Understand the Problem
The image shows two problems related to finding the x and y intercepts of a linear equation. The first problem asks to find the x-intercept, and it provides the solution by setting y=0 and solving for x. The second problem asks to find the y-intercept, and it provides the solution by setting x=0 and solving for y.
Answer
$x$-intercept: $(4, 0)$ $y$-intercept: $(0, 8)$
Answer for screen readers
The $x$-intercept is $(4, 0)$ and the $y$-intercept is $(0, 8)$.
Steps to Solve
- Find the x-intercept
To find the $x$-intercept, we set $y = 0$ in the equation $-2x + 8 = y$ and solve for $x$. $$ 0 = -2x + 8 $$
- Solve for x
Add $2x$ to both sides of the equation: $$ 2x = 8 $$ Divide both sides by 2: $$ x = \frac{8}{2} = 4 $$ The $x$-intercept is the point $(4, 0)$.
- Find the y-intercept
To find the $y$-intercept, we set $x = 0$ in the equation $-2x + 8 = y$ and solve for $y$. $$ y = -2(0) + 8 $$
- Solve for y
Simplify the equation: $$ y = 0 + 8 = 8 $$ The $y$-intercept is the point $(0, 8)$.
The $x$-intercept is $(4, 0)$ and the $y$-intercept is $(0, 8)$.
More Information
The points where a line crosses the x and y axes are called the x and y intercepts, respectively. Setting $y=0$ allows one to solve for the $x$-intercept. Similarly, setting $x=0$ allows one to solve for the $y$-intercept.
Tips
A common mistake is to mix up the x and y values when stating the intercepts. The x-intercept is where the line crosses the x-axis, meaning the y-value is 0. The y-intercept is where the line crosses the y-axis, meaning the x-value is 0.
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