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Mashutka [201]
3 years ago
11

"Write two equations: one parallel, one perpendicular to (5,-2) y= 1/5x-3

Mathematics
2 answers:
guajiro [1.7K]3 years ago
7 0

Answer:

For parallel:

gradient is 1/5

y = mx + c

consider (5, -2):

- 2 = ( \frac{1}{5}  \times 5) + c \\  - 2 = 1 + c \\ c =  - 3

{ \boxed{ \bf{equation : y =  \frac{1}{5}x - 3 }}}

For perpendicular:

gradient, m1:

m _{1} \times m_{2} =  - 1 \\ m _{1} \times  \frac{1}{5}  =  - 1 \\  \\ m _{1} =  - 5

gradient = -5

y = mx + c \\  - 2 = (5 \times -  5) + c \\  - 2 =  - 25 + c \\ c =  23

{ \boxed{ \bf{equation :y =  - 5x + 23 }}}

iren [92.7K]3 years ago
5 0

Answer:

Parallel: y=\displaystyle \frac{1}{5}x-3

Perpendicular: y=-5x+23

Step-by-step explanation:

Hi there!

<u>What we must know:</u>

  • Slope intercept form: y=mx+b where <em>m</em> is the slope and <em>b</em> is the y-intercept (the value of y when the line crosses the y-axis)
  • Parallel lines always have the same slope
  • Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2, -6/7 and 7/6)

<u>Finding the Parallel Line</u>

y=\displaystyle \frac{1}{5} x-3

Given this equation, we can identify that its slope (<em>m</em>) is \displaystyle \frac{1}{5}. Because parallel lines always have the same slope, the slope of the line we're currently solving for would be \displaystyle \frac{1}{5} as well. Plug this into y=mx+b:

y=\displaystyle \frac{1}{5}x+b

Now, to find the y-intercept, plug in the given point (5,-2) and solve for <em>b</em>:

-2=\displaystyle \frac{1}{5}(5)+b\\\\-2=1+b\\-2-1=b\\-3=b

Therefore, the y-intercept is -3. Plug this back into y=\displaystyle \frac{1}{5}x+b:

y=\displaystyle \frac{1}{5}x+(-3)\\\\y=\displaystyle \frac{1}{5}x-3

Our final equation is y=\displaystyle \frac{1}{5}x-3.

<u>Finding the Perpendicular Line</u>

y=\displaystyle \frac{1}{5} x-3

Again, the slope of this line is \displaystyle \frac{1}{5}. The slopes of perpendicular lines are negative reciprocals, so the slope of the line we're solving for would be -5. Plug this into y=mx+b:

y=-5x+b

To find the y-intercept, plug in the point (5,-2) and solve for <em>b</em>:

-2=-5(5)+b\\-2=-25+b\\-2+25=b\\23=b

Therefore, the y-intercept is 23. Plug this back into y=-5x+b:

y=-5x+23

Our final equation is y=-5x+23.

I hope this helps!

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