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 derive the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's calculate the slope using the given points (0, 4) and (1, 8):
slope = (change in y) / (change in x)
= (8 - 4) / (1 - 0)
= 4 / 1
= 4
Next, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope we calculated into the equation:
y = 4x + b
Now, we need to find the y-intercept (b). We can use one of the given points (0, 4) to solve for b.
4 = 4(0) + b
4 = b
Therefore, 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 write the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's calculate the slope using the given points (0, 2) and (1, -1):
slope = (change in y) / (change in x)
= (-1 - 2) / (1 - 0)
= -3 / 1
= -3
Next, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope we calculated into the equation:
y = -3x + b
Now, we need to find the y-intercept (b). We can use one of the given points (0, 2) to solve for b.
2 = -3(0) + b
2 = b
Therefore, the equation of the line in slope-intercept form is y = -3x + 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 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 write the equation of the line in slope-intercept form, we need to find the slope and the y-intercept.
First, let's calculate the slope using the given points (0, -2) and (3, 0):
slope = (change in y) / (change in x)
= (0 - (-2)) / (3 - 0)
= 2 / 3
Next, we can use the slope-intercept form of a line, which is y = mx + b, where m is the slope and b is the y-intercept. We can substitute the slope we calculated into the equation:
y = (2/3)x + b
Now, we need to find the y-intercept (b). We can use one of the given points (0, -2) to solve for b.
-2 = (2/3)(0) + b
-2 = b
Therefore, 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
.
The slope of the equation y = -2x + 2 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 of the equation y = 34x - 2 is (0, -2).
To derive the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept of the line.
Step 1: Find the slope of the line.
The slope of a line can be calculated using the formula:
slope = (change in y)/(change in x)
In this case, we have two points on the line: (0,4) and (1,8).
change in y = 8 - 4 = 4
change in x = 1 - 0 = 1
slope = 4/1 = 4
Step 2: Find the y-intercept of the line.
The y-intercept is the point where the line crosses the y-axis. In this case, we can see that the line passes through the point (0,4). Since the x-coordinate of this point is 0, the y-intercept is 4.
Step 3: Write the equation of the line.
Now that we have the slope (m = 4) and the y-intercept (b = 4), we can write the equation of the line in slope-intercept form, which is:
y = mx + b
Substituting the values, we get:
y = 4x + 4
So, the equation of the line in slope-intercept form is y = 4x + 4.