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 3 x plus 4
y=−3x−4
y equals negative 3 x minus 4
y=3x−4
y equals 3 x minus 4
To derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
Looking at the graph, we can see that the line passes through the points (0, -4) and (1, -1).
We can calculate the slope (m) using the formula:
m = (change in y) / (change in x)
m = (-1 - (-4)) / (1 - 0)
m = (-1 + 4) / 1
m = 3 / 1
m = 3
Now that we have the slope, we can use the point-slope form of the equation to find the equation of the line:
y - y1 = m(x - x1)
Using the point (0, -4):
y - (-4) = 3(x - 0)
y + 4 = 3x
Rewriting the equation in slope-intercept form (y = mx + b), we can isolate y:
y = 3x - 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 given points (0,-4) and (1,-1), we can calculate the slope as follows:
slope = (change in y) / (change in x)
= (-1 - (-4)) / (1 - 0)
= 3/1
= 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), the equation becomes:
y - (-4) = 3(x - 0)
y + 4 = 3x
Finally, rearranging the equation to the slope-intercept form (y = mx + b), where b represents the y-intercept:
y = 3x - 4
Therefore, the equation of the line in slope-intercept form is:
y = 3x - 4