Questions: Question 8 OMark this question Consider the equation y=15-4x. Which of the following is a graph of this equation?

Transcript text: Question 8 OMark this question Consider the equation $y=15-4 x$. Which of the following is a graph of this equation?

Solution

Solution Steps

To determine which graph represents the equation $ y = 15 - 4x $, we need to identify the key characteristics of the line. This equation is in the slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept. Here, the slope $ m $ is $-4$ and the y-intercept $ b $ is $15$. The line will cross the y-axis at $ (0, 15) $ and will have a downward slope, decreasing by 4 units in $ y $ for every 1 unit increase in $ x $.

Step 1: Identify the Equation Form

The given equation is $ y = 15 - 4x $. This is in the slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

Step 2: Determine the Slope and Y-Intercept

From the equation $ y = 15 - 4x $, we identify:

The slope $ m = -4 $.
The y-intercept $ b = 15 $.

Step 3: Analyze the Line Characteristics

The line will:

Cross the y-axis at the point $ (0, 15) $.
Have a downward slope, indicating that for every increase of 1 unit in $ x $, $ y $ decreases by 4 units.

Step 4: Plot Key Points

To further understand the line, calculate a few key points:

When $ x = 0 $, $ y = 15 - 4(0) = 15 $.
When $ x = 1 $, $ y = 15 - 4(1) = 11 $.
When $ x = -1 $, $ y = 15 - 4(-1) = 19 $.

Step 5: Sketch the Graph

Using the points $(0, 15)$, $(1, 11)$, and $(-1, 19)$, sketch the line. The line should pass through these points and have a negative slope.

Final Answer

The graph of the equation $ y = 15 - 4x $ is a straight line with a y-intercept at $ (0, 15) $ and a slope of $-4$. The line decreases as $ x $ increases. The correct graph will reflect these characteristics.

$\boxed{\text{The graph is a straight line with a negative slope and y-intercept at } (0, 15).}$

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