Graphing Linear Equations Unit Test

Question

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Question
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)

Answer 1

First, we need to find the slope of the line from the plotted points. The slope formula is:

m = (y2 - y1) / (x2 - x1)

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

m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5

Next, we can use the point-slope form of a linear equation to find the equation of the line:

y - y1 = m(x - x1)

Using the point (0, -2) and the slope 5:

y - (-2) = 5(x - 0)
y + 2 = 5x

Now, we can rewrite this equation in slope-intercept form (y = mx + b):

y = 5x - 2

Therefore, the equation of the line in slope-intercept form is y = 5x - 2.