To find the equation of a line that is parallel to the given equation, we need to determine the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
In the given equation, y = -3x + 5, the slope is -3.
Since the desired line is parallel to the given one, it will have the same slope of -3.
Now we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
Using the point (-8, -7), we have:
y - (-7) = -3(x - (-8))
y + 7 = -3(x + 8)
Expanding and simplifying:
y + 7 = -3x - 24
Now we can rewrite the equation in slope-intercept form by isolating y:
y = -3x - 24 - 7
y = -3x - 31
Therefore, the equation of the line that passes through the point (-8, -7) and is parallel to the graph of y = -3x + 5 is y = -3x - 31.
Write an equation in slope-intercept form of the line that passes through the given point and is parallel to the graph of the given equation.
(-8, -7); y = -3x + 5
9 answers
Determine whether the pair of lines is parallel, perpendicular, or neither.
x - 2y = -9
y = 9x - 5
x - 2y = -9
y = 9x - 5
To determine whether the pair of lines is parallel, perpendicular, or neither, we need to compare the slopes of the two lines.
First, let's convert both equations to slope-intercept form (y = mx + b).
For the equation x - 2y = -9:
x - 2y = -9
-2y = -x - 9
y = (1/2)x + 9/2
This line has a slope of 1/2.
For the equation y = 9x - 5, we can see that the slope is 9.
Since the slopes of the two lines are different (1/2 and 9), the lines are neither parallel nor perpendicular.
First, let's convert both equations to slope-intercept form (y = mx + b).
For the equation x - 2y = -9:
x - 2y = -9
-2y = -x - 9
y = (1/2)x + 9/2
This line has a slope of 1/2.
For the equation y = 9x - 5, we can see that the slope is 9.
Since the slopes of the two lines are different (1/2 and 9), the lines are neither parallel nor perpendicular.
Write an equation in slope-intercept form of the line that passes through the given point and is perpendicular to the graph of the given equation.
(-3,6); y = 1/3x - 4
(-3,6); y = 1/3x - 4
To find the equation of a line that is perpendicular to the given equation, we need to determine the negative reciprocal of the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
In the given equation, y = 1/3x - 4, the slope is 1/3.
The negative reciprocal of 1/3 is -3.
Now we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
Using the point (-3, 6), we have:
y - 6 = -3(x - (-3))
y - 6 = -3(x + 3)
Expanding and simplifying:
y - 6 = -3x - 9
Now we can rewrite the equation in slope-intercept form by isolating y:
y = -3x - 9 + 6
y = -3x - 3
Therefore, the equation of the line that passes through the point (-3, 6) and is perpendicular to the graph of y = 1/3x - 4 is y = -3x - 3.
In the given equation, y = 1/3x - 4, the slope is 1/3.
The negative reciprocal of 1/3 is -3.
Now we can use the point-slope form of a line to find the equation. The point-slope form is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line.
Using the point (-3, 6), we have:
y - 6 = -3(x - (-3))
y - 6 = -3(x + 3)
Expanding and simplifying:
y - 6 = -3x - 9
Now we can rewrite the equation in slope-intercept form by isolating y:
y = -3x - 9 + 6
y = -3x - 3
Therefore, the equation of the line that passes through the point (-3, 6) and is perpendicular to the graph of y = 1/3x - 4 is y = -3x - 3.
Write an equation for the following translation of y = |x|
5 units up
5 units up
To write an equation for the translation of y = |x| that is 5 units up, we need to modify the original equation by adding 5 to the y-coordinate of each point.
The equation y = |x| represents the absolute value function, which is symmetrical around the x-axis.
To shift this function 5 units up, we need to add 5 to every y-coordinate. The equation becomes:
y = |x| + 5
The equation y = |x| represents the absolute value function, which is symmetrical around the x-axis.
To shift this function 5 units up, we need to add 5 to every y-coordinate. The equation becomes:
y = |x| + 5
Write an equation for the following translation of y = -|x|.
15 units up
15 units up
To write an equation for the translation of y = -|x| that is 15 units up, we need to modify the original equation by adding 15 to the y-coordinate of each point.
The equation y = -|x| represents the reflection of the absolute value function across the x-axis.
To shift this reflected function 15 units up, we still add 15 to every y-coordinate. The equation becomes:
y = -|x| + 15
The equation y = -|x| represents the reflection of the absolute value function across the x-axis.
To shift this reflected function 15 units up, we still add 15 to every y-coordinate. The equation becomes:
y = -|x| + 15