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
y
=
m
x
+
b
?

(1 point)
Responses

y=3x−3
y
=
3
x
−
3
y equals 3 x minus 3

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

y=3x+3
y
=
3
x
+
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 first need to determine the slope \( m \) and the y-intercept \( b \).

Given the points \( (0, -3) \) and \( (1, 0) \):

1. Find the slope \( m \): The slope \( m \) is calculated using the formula:

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

   Substituting in our points \( (0, -3) \) and \( (1, 0) \):

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

2. Using point-slope form to find \( b \): Now, we can use one of the points to find the y-intercept \( b \). We can use the point \( (0, -3) \):

   \[ y = mx + b \] Plugging in \( x = 0 \) and \( y = -3 \):

   \[ -3 = 3(0) + b \implies -3 = b \]

3. Form the equation: Now we have \( m = 3 \) and \( b = -3 \), so we can write the equation of the line as:

   \[ y = 3x - 3 \]

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

The final answer is:
y = 3x - 3.