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
y=−3x−4
y equals negative 3 x minus 4
y=3x+4
y equals 3 x plus 4
y=3x−4
y equals 3 x minus 4
3x−y=4
3 x minus y equals 4
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The correct answer is y=3x-4.
To determine the equation of the line in slope-intercept form, we need to find the slope and y-intercept.
From the graph, we can see that the line passes through the points (0, -4) and (1, -1).
The slope, denoted by m, can be calculated using the formula:
m = (change in y) / (change in x)
We can calculate the change in y as -1 - (-4) = 3, and the change in x as 1 - 0 = 1.
So, the slope is m = 3/1 = 3.
Next, we can substitute the slope and one of the points into the slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.
Using the point (0, -4):
-4 = 3(0) + b
-4 = b
Therefore, the y-intercept is b = -4.
Now we can write the equation of the line in slope-intercept form:
y = 3x - 4.
So, the correct answer is:
y = 3x - 4.