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
3x−y=4
3 x minus y equals 4
y=3x−4
y equals 3 x minus 4
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To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
Looking at the two given points, (0, -4) and (1, -1), we can calculate the slope using the formula:
slope = (change in y)/(change in x)
slope = (-1 - (-4)) / (1 - 0) = 3 / 1 = 3
Now, we have the slope, which is 3, and we can use either of the given points to find the y-intercept. Let's use the point (0, -4).
Using the slope-intercept form y = mx + b, where m is the slope and b is the y-intercept, we substitute the values:
-4 = 3(0) + b
-4 = 0 + b
b = -4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
From the graph, we can see that the line passes through the points (0, -4) and (1, -1).
The slope (m) of the line can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates (0, -4) and (1, -1) into the formula:
m = (-1 - (-4)) / (1 - 0)
m = 3/1
m = 3
The y-intercept (b) of the line can be determined by substituting the coordinates of any point (x, y) on the line into the slope-intercept form of a line:
y = mx + b
Using the point (0, -4):
-4 = 3(0) + b
-4 = 0 + b
b = -4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4