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)
y=
x-

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 \(b\).

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

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

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

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

   Plugging in the values:

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

2. Find the y-intercept (b): The y-intercept \(b\) is the value of \(y\) when \(x = 0\). From the point \((0, -2)\), we see that when \(x = 0\), \(y = -2\). Therefore, \(b = -2\).

3. Write the equation of the line: Now that we have the slope and the y-intercept, we can write the equation in slope-intercept form:

   \[ y = 5x - 2 \]

Thus, the equation of the line is:

\[ y = 5x - 2 \]