Question

Please help me!! Choose the equation of the line passing through the point (-4, -2) and perpendicular to y = -x + 6.

Answer 1

Answer choices:
a) y = -x + 6
b) y = x - 6
c) y = -x - 2
d) y = x + 2

Answer 2

Lets start with A.

To know if the point goes through, we would plug in the X value into A and see if we get the Yvalue, -2

Answer 3

So like y = -4 + 6?

Answer 4

Wait you also have to find the gradient for perpendicular line

Answer 5

so the gradient for perpendicular line is 1
giving us the equation y = x+c

Answer 6

What's a gradient? I don't think that was in my lessons.

Answer 7

Would you know how the graph of -X+6 would look like? Have a calculator handy?

Answer 8

I don't know what it would look like but I have a calculator

Answer 9

https://www.desmos.com/calculator

Here, use this one to graph it

Answer 10

ok i graphed it

Answer 11

@FortyTheRapper

Answer 12

I'm pretty sure you need to find the new y-intercept first as a start to getting the new equation

Try plugging in the coordinates first to find the new "b".

Answer 13

I don't really understand what that means, I'm not good with this stuff /:

Answer 14

What I mean is...You want to get rid of the original y-intercept, (in this case, it's 6), and use the x and y values given to replace the x and y in the original equation.

Answer 15

could you give me an example?

Answer 16

The perpendicular equation of a line means that an equation of a line that meets up with the original line at a 90-degree angle. All you have to do to find the perpendicular of a slope is to reverse it, or known as reciprocal. It just makes the integer and fraction of the slope the opposite of it's original value.

Here's an example. An equation of Line A is \[y=5x+2\] and passes through point C (3,1)
Determine the equation of Line B that is perpendicular to Line A
1. Leave the y-int out
\[y=5x+b\]
2. Reverse the slope (called the reciprocal)
\[y=-\frac{ 1 }{ 5 }x + b\]
3. Plug in the x and y coordinates
We know that y = 1 and x = 3, so..
\[1=\frac{ 1 }{ 5 }(3) + b\]
4. Solve for b. I turned 3 into a fraction of 3 over 1 to make it easier to multiply.
\[1=-\frac{ 1 }{ 5 }(\frac{ 3 }{ 1 }) + b\]
\[1=-\frac{ 3 }{ 5 } + b\]
Whatever you do on the right side, you do the same on the left side. In this case, I added 3/5 to -3/5 on the right, so I did the same on the left.
\[1+\frac{ 3 }{ 5 }=b\]
\[1\frac{ 3 }{ 5 }=b\]
Now that you have all of the values, you can determine the new equation of Line B that is perpendicular to Line A. Use the reciprocal of the original slope mentioned earlier for the new equation.
\[y=mx+b\]
\[y=-\frac{ 1 }{ 5 }x+1\frac{ 3 }{ 5 }\]

Answer 17

Ok i get it

Answer 18

So is it 6 = -4 + b? If not, I'm sorry

Answer 19

You get rid of the 6 that replaced b. The actual way to do it is -2 = -4+b. Since 1 is invisible infront of -x, all you have to do is flip the integer of itself. Think if -x as\[-\frac{ 1 }{ 1 }x\]
And when you use the reciprocal of it, it turns into x, or think of it as \[\frac{ 1 }{ 1 }x\]
But, don't write it down that way. The best way to represent those two slopes is -x (for the first one), or x (for the second one)