Question

Indicate in standard form the equation of the line passing through the given point and having the given slope.

B(6, 2), m = -1/2

A(4, 1), B(5, 2)

M(0, 6), N(6, 0)

D(5, -2) m = 2/5

A(5, 5), m = 3

B(0, 0), C(4, -4)

P(6, 2), Q(8, -4)

E(-2, 2), F(5, 1)

Answer 1

When I try to write the standard form of an equation, I first try to start off by writing it in slope-intercept form. And then I can move certain terms around to make it into \(ax + by =c\).

Answer 2

I will help you with the first problem and you can use a very similar approach for the other problems.

Answer 3

We know that the slope-intercept form is: \(y = mx + b\).

We can substitute the information that we know to be true based on what is given to us.
\( y = -\frac{1}{2}x + b\)
We can add in the 6 for the x and 2 for the y.
\( 2 = -\frac{1}{2}(6) + b\)

Answer 4

Sorry, I'm here.

Answer 5

I've already got answers but it didn't accept them.

Answer 6

For the first one I got X+20y=46, however that didn't fit.

Answer 7

Using \(2 = -\frac{1}{2}(6) + b\) we can find out what the b value (or the y-intercept) is.

\(2 = -\frac{1}{2}(6) + b\)
\(2 = -3 + b\)
\(2 \color{red}{+3} = -3 \color{red}{+3} + b\)
\(5 = b\)

Therefore, the slope-intercept form for the first problem is \(y = -\frac{1}{2}x + 5\)

We need to make sure that it looks like \(ax + by = c\).

So it would be a good idea to move \[-\frac{1}{2}x\] to the other side of the equal sign with \(y\) to get:
\(\large \color{green}{\frac{1}{2}x + y = 5}\)

Answer 8

It will not allow me to put fractions or decimals either.

Answer 9

That sounds weird. But if it's so, then maybe you can multiply all of the terms by 2 to get rid of the fraction. \[2(\frac{1}{2}x + y = 5)\] Then you should get \[x + 2y = 10\]

Answer 10

Alright. That makes sense, I'll try it.

Answer 11

Let me know if it works.

Answer 12

It accepted it. Also for the next question I got X-3-y and it rejected the 3 and y. Do I just need to re-arrange it?

Answer 13

Let me see.

Answer 14

The slope-intercept form for that problem is \(y = x -3\). If you rearrange it standard form you should get \(-x + y = -3\).

Answer 15

And X can't be negative correct?

Answer 16

Usually people don't like to have a negative \(x\). In that case, then multiply all of the terms by -1 to remove the negative from the x. You should then get \(x - y = 3\)

Answer 17

For the next one I got x+y=5 and it rejected the 5

Answer 18

It should be \(x + y = 6\).

Answer 19

I have to go now. Sorry about that. But I have one tip. Just so that you can double-check your answer, make sure that you substitute the x and the y values into the standard form equation and then check whether it is true or not.

Answer 20

Alright, thanks for helping me!