Ask a New Question
Menu

Use the image to answer the question.

A coordinate plane shows the x-axis ranging from negative 9 to 9 in increments of 1 and the y-axis ranging from 11 to negative 11 in increments of 1. A line with arrows at both ends joins two plotted points.
The coordinates of the plotted points are as follows: left parenthesis 0 comma 3 right parenthesis, and left parenthesis 3 comma 2 right parenthesis.
Is this the correct graph of y=−13x+4
?(1 point)
Responses

Yes, it is the correct graph because this graph has a y
-intercept of (0,4)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 4 right parenthesis .

Yes, it is the correct graph because this graph has a y
-intercept of (0,3)
.
Yes, it is the correct graph because this graph has a y -intercept of left parenthesis 0 comma 3 right parenthesis .

No, it is not the correct graph because this graph has a positive slope.
No, it is not the correct graph because this graph has a positive slope.

No, it is not the correct graph because this graph used (0,3)
as the y
-intercept.
No, it is not the correct graph because this graph used left parenthesis 0 comma 3 right parenthesis as the y -intercept.
Skip to navigation

1 answer

To determine if the line on the graph represents the equation \( y = -13x + 4 \), we need to analyze its properties: specifically, the slope and the y-intercept.

  1. Y-Intercept: The y-intercept of the equation \( y = -13x + 4 \) is \( (0, 4) \). This is where the line crosses the y-axis.

  2. Points Given: The plotted points on the graph are \( (0, 3) \) and \( (3, 2) \). The y-coordinate of the first point shows that the graph intercepts the y-axis at \( (0, 3) \), which is different from the calculated y-intercept of \( (0, 4) \).

  3. Slope: The slope can also be calculated using the two points:

    • The change in y (Δy) between the points (2 - 3 = -1)
    • The change in x (Δx) between the points (3 - 0 = 3)
    • Slope (m) = Δy / Δx = -1 / 3, which is positive.

Since the graph shows a y-intercept at (0, 3) instead of (0, 4) and the slope calculation indicates a negative slope, these facts lead to the conclusion:

The correct response is: No, it is not the correct graph because this graph used (0, 3) as the y-intercept.