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 2 right parenthesis and left parenthesis 1 comma 3 right parenthesis.

Use the graph to derive the equation of the line in slope-intercept form.

(1 point)

Answer 1

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

1. Finding the Slope (m): The slope (m) is calculated using the formula:

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

   For the points (0, -2) and (1, 3):

   • \( (x_1, y_1) = (0, -2) \)
   • \( (x_2, y_2) = (1, 3) \)

   Plugging in these values:

   \[ m = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]

   So, the slope \( m = 5 \).

2. Finding the Y-Intercept (b): The y-intercept (b) is the value of y when x = 0. From the point (0, -2), we can see that when x is 0, y is -2.

   Thus, \( b = -2 \).

3. Writing the Equation: Now, we can substitute the slope and y-intercept into the slope-intercept form of the equation:

   \[ y = mx + b \] \[ y = 5x - 2 \]

The equation of the line in slope-intercept form is:

\[ \boxed{y = 5x - 2} \]