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.
(-6,-3); y = -5x+5
Write an equation for the line in slope-intercept form. (Simplify your answer. Use integers or fractions for any numbers in the equation.)
A line that is parallel to the graph of y = -5x + 5 will have the same slope. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope of the given equation is -5. Therefore, the equation for the line that passes through the point (-6, -3) and is parallel to the given equation is:
y = -5x + b
To find b, substitute the coordinates of the given point into the equation:
-3 = -5(-6) + b
Simplifying,
-3 = 30 + b
Subtracting 30 from both sides,
-33 = b
Therefore, the equation of the line in slope-intercept form is:
y = -5x - 33
Determine whether the pair of lines is parallel, perpendicular, or neither. x-4y=-6 y=9x-2
A.
More information is needed.
B.
The two lines are perpendicular.
C.
The two lines are parallel.
D.
The two lines are neither parallel nor perpendicular.
To determine if the pair of lines is parallel or perpendicular, we need to compare the slopes of the two lines.
The given equations are:
1) x - 4y = -6
2) y = 9x - 2
To determine the slope of a line in the form "ax + by = c", we can rearrange the equation to solve for y and then compare the coefficients of x.
1) x - 4y = -6
Rearranging this equation to solve for y:
4y = x + 6
y = (1/4)x + 3/2
Comparing the coefficient of x, we see that the slope of line 1 is 1/4.
2) y = 9x - 2
Comparing the coefficient of x, we see that the slope of line 2 is 9.
Since the slopes of the two lines are not equal and not negative reciprocals of each other, the two lines are neither parallel nor perpendicular.
Therefore, the correct answer is:
D. The two 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.
(-4,6); y=1/4x-1
Write an equation for the perpendicular line in slope-intercept form
(Simplify your answer. Use integers or fractions for any numbers in the equation.).
A line that is perpendicular to the graph of y = (1/4)x - 1 will have a negative reciprocal slope. The perpendicular line will have a slope of -4, since the slope of the given equation is 1/4.
The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept.
In this case, the slope of the perpendicular line is -4. To find the equation of the line that passes through the point (-4, 6) and has a slope of -4, we can substitute these values into the slope-intercept form:
y = mx + b
6 = -4(-4) + b
Simplifying,
6 = 16 + b
6 - 16 = b
-10 = b
Therefore, the equation of the perpendicular line in slope-intercept form is:
y = -4x - 10
Write an equation for the following translation of y = |x|.
5 unit down
y =
(Simplify your answer.)
To translate the graph of y = |x| five units down, we need to subtract 5 from the equation.
The equation for the translated graph is:
y = |x| - 5
Write an equation for the following translation of y=-|x|.
1 unit down
y = (simplify your answer)
To translate the graph of y = -|x| one unit down, we need to subtract 1 from the equation.
The equation for the translated graph is:
y = -|x| - 1