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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 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

−3x−y=3
negative 3 x minus y equals 3

y=−3x−3
y equals negative 3 x minus 3

y=3x+3
y equals 3 x plus 3

y=3x−3

Answer 1

To find the equation of the line in the form \( y = mx + b \), we need to determine the slope \( m \) and the y-intercept \( b \) based on the points given: \( (0, -3) \) and \( (1, 0) \).

Step 1: Calculate the slope (m)

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

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

Using the points \( (0, -3) \) as \( (x_1, y_1) \) and \( (1, 0) \) as \( (x_2, y_2) \):

\[ m = \frac{0 - (-3)}{1 - 0} = \frac{0 + 3}{1} = \frac{3}{1} = 3 \]

Step 2: Determine the y-intercept (b)

To find the y-intercept \( b \), we can use the point \( (0, -3) \), which directly gives us:

\[ b = -3 \]

Step 3: Write the equation

Now we can write the equation of the line in slope-intercept form \( y = mx + b \):

\[ y = 3x - 3 \]

Thus, the correct response is:

\( y = 3x - 3 \)