Question

place the correct option in each empty space to complete the table. what are the slope, m, and the x - and y - intercepts of the graph of the function $y = -\frac{1}{2}x - 3$? table with columns characteristic (m, y - intercept, x - intercept) and value (empty boxes) options: -3, $-\frac{1}{2}$, $\frac{1}{2}$, 3, $(-6, 0)$, $(-\frac{1}{2}, 0)$, $(0, -3)$, $(0, -\frac{1}{2})$

Explanation:

Step1: Find the slope \( m \)

The function is in slope - intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the \( y \)-intercept. For the function \( y=-\frac{1}{2}x - 3 \), comparing with \( y = mx + b \), we can see that \( m=-\frac{1}{2} \).

Step2: Find the \( y \)-intercept

The \( y \)-intercept is the point where \( x = 0 \). Substitute \( x = 0 \) into the equation \( y=-\frac{1}{2}x - 3 \). We get \( y=-\frac{1}{2}(0)-3=-3 \). So the \( y \)-intercept is the point \( (0, - 3) \).

Step3: Find the \( x \)-intercept

The \( x \)-intercept is the point where \( y = 0 \). Set \( y = 0 \) in the equation \( y=-\frac{1}{2}x - 3 \). Then we have the equation \( 0=-\frac{1}{2}x - 3 \).
Add 3 to both sides: \( 3=-\frac{1}{2}x \).
Multiply both sides by - 2: \( x=-6 \). So the \( x \)-intercept is the point \( (-6,0) \).

Answer:

• For \( m \): \( -\frac{1}{2} \)
• For \( y \)-intercept: \( (0, - 3) \)
• For \( x \)-intercept: \( (-6,0) \)