Use the image to answer the question.

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

y=−3x−3
y equals negative 3 x minus 3

y=3x−3
y equals 3 x minus 3

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

−3x−y=3
negative 3 x minus y equals 3
Remainin

Answer 1

To determine the equation of the line passing through the points (0, -3) and (1, 0), we can follow these steps:

1. Calculate the slope (m): The slope \( m \) is calculated using the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Here \( (x_1, y_1) = (0, -3) \) and \( (x_2, y_2) = (1, 0) \).

   Plugging in the values: \[ m = \frac{0 - (-3)}{1 - 0} = \frac{3}{1} = 3 \]

2. Use the point-slope form to find the y-intercept (b): We can use one of the points, (0, -3), to find \( b \). The formula for the line in slope-intercept form is: \[ y = mx + b \] Substituting x=0 and y=-3 into the equation to solve for \( b \): \[ -3 = 3(0) + b \implies b = -3 \]

3. Write the equation: Now that we have \( m = 3 \) and \( b = -3 \), we can write the equation of the line: \[ y = 3x - 3 \]

So, the correct answer is:

y = 3x - 3.