Ask a New Question
Menu

Use the image to answer the 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-
Skip to navigation

1 answer

To derive the equation of the line in slope-intercept form (y = mx + b), we first need to determine the slope (m) of the line using the two points given: (0, -2) and (1, 3).

  1. Calculate the slope (m): \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-2)}{1 - 0} = \frac{3 + 2}{1} = \frac{5}{1} = 5 \]

  2. Use the slope and one of the points to find the y-intercept (b). We'll use the point (0, -2): \[ y = mx + b \] Substituting the point into the equation: \[ -2 = 5(0) + b \quad \Rightarrow \quad -2 = b \]

  3. Now plug in the slope and the y-intercept into the slope-intercept form: \[ y = 5x - 2 \]

Thus, the equation of the line in slope-intercept form is:

\[ y = 5x - 2 \]