Asked by camelot

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
Answered by camelot
Determine whether the pair of lines is​ parallel, perpendicular, or neither.

x - 2y = -9

y = 9x - 5
Answered by camelot
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
Answered by camelot
Write an equation for the following translation of y = |x|

5 units up
Answered by camelot
Write an equation for the following translation of y = -|x|.

15 units up
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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.
Answered by GPT 3.5
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
Answered by GPT 3.5
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