First, the equation needs to be put into slope-intercept form, which is y = -4/5x + 7/5. Then, you need to know what parallel and perpendicular lines are. REMEBER, parallel lines have the same slope, and perpendicular lines have slopes whose product equal -1. You just need to substitute. For the parallel line, -2 = -4/5(4) + b, and b = 6/5, so y = -4/5x + 6/5. For the perpendicular line, the slope is 5/4. Now substitute. -2 = 5/4(4) + b, and b = -7, so y = 5/4x -7.
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Step-by-step explanation:
Look at the photo below for the details.
The equation of the perpendicular line is y + 7 = -1/7(x - 3)
<h3>How to determine the line equation?</h3>
The equation is given as
y = 7x + 14
Also, from the question
The point is given as
Point = (3, -7)
The equation of a line can be represented as
y = mx + c
Where
Slope = m
By comparing the equations, we have the following
m = 7
This means that the slope of y = 7x + 14 is 7
So, we have
m = 7
The slopes of perpendicular lines are opposite reciprocals
This means that the slope of the other line is -1/7
The equation of the perpendicular lines is then calculated as
y = m(x - x₁) +y₁
Where
m = -1/7
(x₁, y₁) = (3, -7)
So, we have
y = -1/7(x - 3) - 7
Evaluate
y = -1/7(x - 3) - 7
Add 7 to both sides
y + 7 = -1/7(x - 3)
Hence, the perpendicular line has an equation of y + 7 = -1/7(x - 3)
Read more about linear equations at
brainly.com/question/4074386
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<span>4. Simplify the expression.
sine of x to the second power minus one divided by cosine of negative x</span>
<span>(1−sin2(x))/(sin(x)−csc(x))<span>
</span>sin2x+cos2x=1</span>
<span>1−sin2x=cos2x<span>
</span>cos2(x)/(sin(x)−csc(x))</span>
<span>csc(x)=1/sin(x)</span>
<span>cos2(x)/(sin(x)− 1/sin(x))= cos2(x)/((sin2(x)− 1)/sin(x))</span>
<span>sin2(x)− 1=-cos2(x)</span>
<span>cos2(x)/(( -cos2(x))/sin(x))
=-sin(x)</span>
<span>
the answer is the letter a)
-sin x
</span><span>
5. Find all solutions in the interval [0, 2π). (6 points)sin2x + sin x = 0</span> using a graphical tool
the solutions
x1=0
x2=pi
<span>x3=3pi/2
the answer is the letter </span><span>
D) x = 0, π, three pi divided by two</span>
Answer: Parallel
I believe that if you set up these equations into y = mx + b form, you're able to notice that the slope is the same for each equation. That causes the answer to be parallel
