Questions: Graphs and Functions Finding x - and y-intercepts of a line given the equation: Basic Find the y-intercept and x-intercept of the line. -x+4 y=8 y -intercept: x-intercept:

Graphs and Functions
Finding x - and y-intercepts of a line given the equation: Basic

Find the y-intercept and x-intercept of the line.
-x+4 y=8
y -intercept:
x-intercept:

Transcript text: Graphs and Functionis Finding $x$ - and $y$-intercepts of a line glven the equation: Basic Find the $y$-intercept and $x$-intercept of the line. \[ -x+4 y=8 \] y -intercept: $\square$ $x$-intercept: $\square$

Solution

Solution Steps

To find the intercepts of the line given by the equation $-x + 4y = 8$:

Y-intercept: Set $x = 0$ and solve for $y$.
X-intercept: Set $y = 0$ and solve for $x$.

Step 1: Find the $y$-intercept

To find the $y$-intercept, we set $x = 0$ in the equation $-x + 4y = 8$: \[ -0 + 4y = 8 \implies 4y = 8 \implies y = \frac{8}{4} = 2 \] Thus, the $y$-intercept is $y = 2$.

Step 2: Find the $x$-intercept

To find the $x$-intercept, we set $y = 0$ in the equation $-x + 4y = 8$: \[ -x + 4(0) = 8 \implies -x = 8 \implies x = -8 \] Thus, the $x$-intercept is $x = -8$.

Final Answer

$\boxed{y = 2}$

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