Questions: Which ordered pair represents the y-intercept of the graph of the equation y=-3x-9? A. (-9,0) B. (-3,0) C. (0,-9) D. (0,-3)

Transcript text: 4.6.3 Quiz: Linear, Quadratic, and Exponential Functions Question 3 of 10 Which ordered pair represents the $y$-intercept of the graph of the equation $y=-3 x-9 ?$ A. $(-9,0)$ B. $(-3,0)$ C. $(0,-9)$ D. $(0,-3)$

Solution

Solution Steps

To find the y-intercept of a linear equation in the form $ y = mx + b $, we need to identify the value of $ b $. The y-intercept is the point where the graph intersects the y-axis, which occurs when $ x = 0 $. Therefore, the ordered pair representing the y-intercept is $ (0, b) $.

Step 1: Identify the Equation Form

The given equation is $ y = -3x - 9 $. This is a linear equation in the slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

Step 2: Determine the Y-Intercept

In the equation $ y = -3x - 9 $, the y-intercept $ b $ is $-9$. The y-intercept is the point where the graph intersects the y-axis, which occurs when $ x = 0 $.

Step 3: Write the Ordered Pair for the Y-Intercept

The ordered pair representing the y-intercept is $ (0, b) $. Substituting the value of $ b $, we get the ordered pair $ (0, -9) $.