Questiona. $y=\frac{-1}{3} x+1$
Choose the correct answer below and, if necessary, fill out the answer box to complete your choice. A. The $x$ -intercept is 3 . B. There is no $x$ -intercept.
Choose the correct answer below and, if necessary, fill out the answer box to complete your choice. A. The $y$ -intercept is $\square$ . B. There is no $y$ -intercept.

Studdy Solution

STEP 1

1. The equation given is in the slope-intercept form $y = mx + b$ .
2. The $x$ -intercept occurs where $y = 0$ .
3. The $y$ -intercept occurs where $x = 0$ .

STEP 2

1. Determine the $x$ -intercept.
2. Determine the $y$ -intercept.

STEP 3

To find the $x$ -intercept, set $y = 0$ in the equation $y = \frac{-1}{3}x + 1$ .
$0 = \frac{-1}{3}x + 1$

STEP 4

Solve for $x$ by isolating $x$ on one side of the equation:
$\frac{-1}{3}x = -1$
Multiply both sides by $-3$ to solve for $x$ :
$x = 3$
Thus, the $x$ -intercept is $x = 3$ .

STEP 5

To find the $y$ -intercept, set $x = 0$ in the equation $y = \frac{-1}{3}x + 1$ .
$y = \frac{-1}{3}(0) + 1$
Simplify the equation:
$y = 1$
Thus, the $y$ -intercept is $y = 1$ .
The correct choices are: - For the $x$ -intercept: A. The $x$ -intercept is 3. - For the $y$ -intercept: A. The $y$ -intercept is $\boxed{1}$ .

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