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 4 right parenthesis and left parenthesis 1 comma 8 right parenthesis.
Derive the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
To calculate the slope, we will use the formula:
m = (change in y) / (change in x)
The change in y = 8 - 4 = 4
The change in x = 1 - 0 = 1
So, the slope (m) = 4/1 = 4.
To calculate the y-intercept (b), we can use the point-slope form of the equation:
y = mx + b
We can substitute the values of one of the given points into the equation and solve for b.
Using the point (0, 4):
4 = 4(0) + b
4 = b
Therefore, the y-intercept (b) is 4.
The equation of the line in slope-intercept form is:
y = 4x + 4.
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 downward line with arrows at both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma 2 right parenthesis and left parenthesis 1 comma negative 1 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
To calculate the slope, we will use the formula:
m = (change in y) / (change in x)
The change in y = -1 - 2 = -3
The change in x = 1 - 0 = 1
So, the slope (m) = -3/1 = -3.
To calculate the y-intercept (b), we can use the point-slope form of the equation:
y = mx + b
We can substitute the values of one of the given points into the equation and solve for b.
Using the point (0, 2):
2 = -3(0) + b
2 = b
Therefore, the y-intercept (b) is 2.
The equation of the line in slope-intercept form is:
y = -3x + 2.
Graphing Equations Practice
Complete this assessment to review what you've learned. It will not count toward your grade.
3 of 53 of 5 Items
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 on both ends is plotted on the graph. The line passes through the plotted points left parenthesis 0 comma negative 2 right parenthesis and left parenthesis 3 comma 0 right parenthesis.
Write the equation of the line in slope-intercept form.
(1 point)
To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b).
To calculate the slope, we will use the formula:
m = (change in y) / (change in x)
The change in y = 0 - (-2) = 2
The change in x = 3 - 0 = 3
So, the slope (m) = 2/3.
To calculate the y-intercept (b), we can use the point-slope form of the equation:
y = mx + b
We can substitute the values of one of the given points into the equation and solve for b.
Using the point (0, -2):
-2 = (2/3)(0) + b
-2 = b
Therefore, the y-intercept (b) is -2.
The equation of the line in slope-intercept form is:
y = (2/3)x - 2.
Given the equation y=−2x+2, what is the slope? Write your answer as an integer.(1 point)
The slope is
-2
Given the equation y=34x−2 what is the y-intercept? Write your answer as an ordered pair.(1 point)
The y-intercept is (
).
The y-intercept is (0, -2)
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 3 x plus 4
y=3x−4
y equals 3 x minus 4
y=−3x−4
y equals negative 3 x minus 4
3x−y=4