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)ResponsesYes, 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.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 .Skip to navigation

Answer 1

To determine whether the graph given corresponds to the equation \( y = -13x + 4 \), we can analyze the slope and y-intercept.

1. Y-Intercept: The y-intercept of the equation \( y = -13x + 4 \) is \( 4 \). Therefore, the point \( (0, 4) \) should be on the graph of the line.

2. Point Analysis: The points plotted on the graph are \( (0, 3) \) and \( (3, 2) \). The y-coordinate of the point \( (0, 3) \) indicates that this graph uses \( (0, 3) \) as a y-intercept instead of \( (0, 4) \).

3. Slope Calculation: To calculate the slope between the two given points \( (0, 3) \) and \( (3, 2) \):

   • Slope \( m \) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2 - 3}{3 - 0} = \frac{-1}{3} \).

   Since the slope is negative, this does not match the slope of \( -13 \), which is significantly steeper.

Given this information, we can conclude that the graph described does not accurately represent the equation \( y = -13x + 4 \). Consequently, the correct response is:

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

Answer 2

Use the image to answer the question.

An illustration of a coordinate plane with four quadrants shows the x-axis ranging from negative 9 to 9 and the y-axis ranging from negative 11 to 11 in increments of 1. A solid downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 1 right parenthesis and left parenthesis 1 comma negative 4 right parenthesis.

Write the equation of the line in slope-intercept form.

(1 point)
Responses

y=−5x−1
y equals negative 5 x minus 1

y=5x+1
y equals 5 x plus 1

−5x−y=−1
negative 5 x minus y equals negative 1

y=−5x+1

Answer 3

To write the equation of the line in slope-intercept form \( y = mx + b \), we need to determine the slope \( m \) using the two points given: \( (0, 1) \) and \( (1, -4) \).

1. Calculate the Slope \( m \): The formula for the slope between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is:

   \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

   Plugging in the coordinates:

   • \( (x_1, y_1) = (0, 1) \)
   • \( (x_2, y_2) = (1, -4) \)

   We have:

   \[ m = \frac{-4 - 1}{1 - 0} = \frac{-5}{1} = -5 \]

2. Find the Y-Intercept \( b \): Since the line passes through the point \( (0, 1) \), we know that the y-intercept \( b \) is \( 1 \).

3. Write the Equation: We now have the slope \( m = -5 \) and y-intercept \( b = 1 \). Thus, the equation of the line in slope-intercept form is:

   \[ y = -5x + 1 \]

Given the options provided, the correct response is:

y = -5x + 1.