Graphing Equations Quick Check
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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 4 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Using the graph, derive the equation of the line in slope-intercept form.
(1 point)
First, determine the slope of the line using the two points provided: (-4,0) and (-1,1).
Slope = (y2 - y1) / (x2 - x1)
Slope = (1 - 0) / (-1 - (-4))
Slope = 1 / 3
Next, use the slope-intercept form of a linear equation, y = mx + b, and substitute the slope and one of the points to solve for the y-intercept, b.
1 = (1/3)(-1) + b
1 = -1/3 + b
b = 4/3
Therefore, the equation of the line in slope-intercept form is y = (1/3)x + 4/3.