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.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's calculate the slope using the given points (0, 4) and (1, 8).
The slope (m) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Substituting the points, we have:
m = (8 - 4)/(1 - 0)
m = 4/1
m = 4
Next, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (0, 4) and the slope we found (m = 4), we substitute these values into the point-slope formula:
y - 4 = 4(x - 0)
Simplifying, we have:
y - 4 = 4x
To express the equation in slope-intercept form (y = mx + b), we rearrange the equation:
y = 4x + 4
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.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's calculate the slope using the given points (0, 2) and (1, -1).
The slope (m) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Substituting the points, we have:
m = (-1 - 2)/(1 - 0)
m = -3/1
m = -3
Next, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (0, 2) and the slope we found (m = -3), we substitute these values into the point-slope formula:
y - 2 = -3(x - 0)
Simplifying, we have:
y - 2 = -3x
To express the equation in slope-intercept form (y = mx + b), we rearrange the equation:
y = -3x + 2
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.
To find the equation of the line in slope-intercept form, we need to determine the slope and the y-intercept.
First, let's calculate the slope using the given points (0, -2) and (3, 0).
The slope (m) is given by the formula:
m = (y2 - y1)/(x2 - x1)
Substituting the points, we have:
m = (0 - (-2))/(3 - 0)
m = 2/3
Next, we can use the point-slope form of a linear equation to find the equation of the line. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (0, -2) and the slope we found (m = 2/3), we substitute these values into the point-slope formula:
y - (-2) = (2/3)(x - 0)
Simplifying, we have:
y + 2 = (2/3)x
To express the equation in slope-intercept form (y = mx + b), we rearrange the equation:
y = (2/3)x - 2
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.
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
The y-intercept of the equation y = 34x - 2 is the point (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.