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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 upward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 3 right parenthesis and left parenthesis 1 comma 0 right parenthesis.

What is the equation of the line in the form y=mx+b
?

(1 point)
Responses

y=−3x−3
y is equal to negative 3 x minus 3 - no response given

y=3x+3
y is equal to 3 x plus 3 - incorrect

−3x−y=3
negative 3 x minus y is equal to 3 - no response given

y=3x−3
y is equal to 3 x minus 3 - no response given
Remaining Attempts : 1
Incorrect

This answer used 3 for the y-intercept.
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1 answer

To find the equation of the line in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \).

  1. Find the slope \( m \):

    • The two points provided are \( (0, -3) \) and \( (1, 0) \).
    • The formula for the slope \( m \) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
    • Using points \( (0, -3) \) as \( (x_1, y_1) \) and \( (1, 0) \) as \( (x_2, y_2) \): \[ m = \frac{0 - (-3)}{1 - 0} = \frac{3}{1} = 3 \]

  2. Find the y-intercept \( b \):

    • The y-intercept \( b \) can be found by using one of the points. Let's use \( (0, -3) \):
    • At \( x = 0 \), \( y = -3 \): \[ b = -3 \]

  3. Combine the results to write the equation:

    • Now we can write the equation of the line using \( m = 3 \) and \( b = -3 \): \[ y = 3x - 3 \]

So, the correct equation of the line is \( y = 3x - 3 \).