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)
Responses
3x−y=4
3 x minus y equals 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y equals 3 x minus 4
y=3x+4
y equals 3 x plus 4
are you sure
Apologies for the confusion. Based on the given information, the correct equation of the line in slope-intercept form is:
y = -3x - 1
To derive the equation of the line in slope-intercept form, we can use the two given points: (0, -4) and (1, -1).
The slope (m) of a line can be found using the formula:
m = (change in y) / (change in x)
Let's calculate the slope:
m = (-1 - (-4)) / (1 - 0)
m = 3 / 1
m = 3
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Using the point (0, -4):
y - (-4) = 3(x - 0)
y + 4 = 3x
Rearranging the equation to slope-intercept form (y = mx + b):
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4
So, the correct answer is:
y = 3x - 4