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 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.

Derive the equation of the line in slope-intercept form.

(1 point)
y
=
x+
Remaining Attempts : 3

1 answer

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

  1. Calculate the slope (m): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the points \((0, 4)\) and \((1, 8)\): \[ m = \frac{8 - 4}{1 - 0} = \frac{4}{1} = 4 \]

  2. Use the slope and a point to find the y-intercept (b): We can use the slope and one of the points (let's use \((0, 4)\)) to find the y-intercept. Recall that y-intercept \(b\) occurs when \(x = 0\). The equation of the line in point-slope form is: \[ y = mx + b \] Plugging in the slope \(m = 4\) and the point \((0, 4)\): \[ 4 = 4(0) + b \ b = 4 \]

  3. Write the final equation in slope-intercept form: Therefore, the equation of the line is: \[ y = 4x + 4 \]

Thus, you would fill in the given form with the resulting values: \[ y = 4x + 4 \]

So the final answer is: \[ y = 4x + 4 \]