Tell whether the lines for the pair of equations are parallel, perpendicular, or neither.
Y=-4/5x+3
4x-5y=-15 (1 point)
Parallel
Perpendicular***
Neither
Write an equation of a line that is perpendicular to the given line and that passes through the given point.
y-2=-1/4(x+3); (-3,5) (1 point)
y=-3x-5***
y=1/4x-6
y=4x+17
y=4x+5
slope of first line = -4/5
for the 2nd:
-5y = -4x - 15
y = (-4/-5)x - 15/-5
y = (4/5)x + 3 ---> slope is +4/5
so they are neither parallel nor perpendicular.
(to be perpendicular, they must be opposite in sign, and flips of each other, not true in your case)
2nd question:
since the slope of the given line is -1/4, the slope of the new line must be +4
so your choices are the last two.
simply try (-3,5) in each
in y = 4x+17
5 = 4(-3) + 17 = 5 , true
in y = 4x + 5 , has to be false
y = 4x + 17
OH ok thx!
To determine whether the lines Y = -4/5x + 3 and 4x - 5y = -15 are parallel, perpendicular, or neither, we can look at the slopes of the lines.
The given line Y = -4/5x + 3 is in slope-intercept form y = mx + b, where m is the slope of the line. In this equation, the slope is -4/5.
To find the slope of the line 4x - 5y = -15, we need to rewrite it in slope-intercept form. We need to isolate y on one side:
4x - 5y = -15
-5y = -4x - 15
y = (4/5)x + 3
Now we can see that the slope of the second line is 4/5.
If lines have slopes that are negative reciprocals of each other, meaning that the slopes multiply to -1, then they are perpendicular.
In this case, the slopes of the lines are -(4/5) and 4/5, which multiply together to give -1. Therefore, the lines are perpendicular.
Answer: Perpendicular.
For the second question, to find an equation of a line that is perpendicular to the given line and passes through the given point (-3,5), we can use the point-slope form of a line.
The given line is y - 2 = -1/4(x + 3).
To find the slope of the given line, we need to rewrite it in slope-intercept form:
y - 2 = -1/4x - 3/4
y = -1/4x - 3/4 + 2
y = -1/4x + 5/4
The slope of the given line is -1/4.
Since a line perpendicular to another line has a slope that is the negative reciprocal of the slope of the given line, the slope of the perpendicular line is 4/1 or 4.
Using the point-slope form, we can write the equation of the perpendicular line passing through (-3,5) as:
y - 5 = 4(x + 3)
Simplifying this equation:
y - 5 = 4x + 12
y = 4x + 17
Answer: y = 4x + 17.
To determine whether two lines are parallel, perpendicular, or neither, we need to compare their slopes.
1. For the first pair of equations, we have:
Equation 1: y = (-4/5)x + 3
Equation 2: 4x - 5y = -15 (we need to convert it to slope-intercept form)
Let's rearrange Equation 2 to slope-intercept form:
4x - 5y = -15
-5y = -4x - 15
y = (4/5)x + 3
Now we can compare the slopes. The slope of Equation 1 is -4/5, and the slope of Equation 2 is 4/5.
Since the slopes are negative reciprocals (opposite signs and upside-down fractions), these lines are perpendicular.
Therefore, the correct answer is perpendicular.
2. To find the equation of a line that is perpendicular to a given line and passes through a given point, follow these steps:
a. First, find the slope of the given line. In this case, the given line is:
y - 2 = (-1/4)(x + 3)
The slope-intercept form of this equation is:
y = (-1/4)x - 3/4
The slope of this line is -1/4.
b. Since we want a line perpendicular to this line, we need a slope that is the negative reciprocal of -1/4, which is 4/1 or 4.
c. Now we use the point (-3, 5) to find the equation. The point-slope form of a line is:
y - y₁ = m(x - x₁)
Substituting the values, we have:
y - 5 = 4(x - (-3))
y - 5 = 4(x + 3)
Now, we can simplify to get the equation in slope-intercept form:
y - 5 = 4x + 12
y = 4x + 17
Therefore, the correct equation of a line perpendicular to the given line and passing through the given point is y = 4x + 17.