Question

How do you put this in point-slope form?
through (4,1), parallel to 2x+5y=10

Answer 1

y-1 = -2/5 (x-4)

Answer 2

Hint:
please note that the equation of the given line, namely:
\[2x + 5y = 10\]
can be rewritten as below:
\[y = - \frac{2}{5}x + 2\]

Answer 3

so, waht is its slope

Answer 4

2/5 @Michele_Laino

Answer 5

no, please it is -2/5

Answer 6

Yeah I just wrote it how you had it in the equation, it was a positive but my mistake. So now that I have the slope, all I do is plug it into the formula?

Answer 7

now, keep in mind that parallel lines have the same slope, so the slope of requested line is m= -2/5, furthermore, you have to apply this equation:
\[y - {y_0} = m(x - {x_0})\]
where:
\[\left( {{x_0},{y_0}} \right) = \left( {4,1} \right)\]

Answer 8

so, please substitute those value of x_0, y_0 and m into the above equation

Answer 9

what do you get?

Answer 10

I'm kinda confused with how I'm multiplying my fraction. This is how I set my problem up: y-1=-2/5(x-4)
distributed: y-1=-2/5x+ ? I know its -2/5 times 4/1. Then I make the denominators alike = -2/5 times 20/5 Am I doing something wrong?

Answer 11

your first step is correct
your second step is:
\[y - 1 = - \frac{2}{5}x + \frac{8}{5}\]
since: \[\left( { - \frac{2}{5}} \right) \cdot \left( { - 4} \right) = \frac{8}{5}\]

Answer 12

Oh I get it now Michele. I was supposed to multiply without like denominators, just straight across. My teacher told me this but I didn't get it

Answer 13

So it's gonna be \[y-1=-\frac{ 2 }{ 5 }x+\frac{ 8 }{ 5 }\]

Answer 14

that's right!

Answer 15

But how do you subtract 1 from \[\frac{ 8 }{ 5 }\]

Answer 16

I mean add 1

Answer 17

please note that you have to add 1 to both sides of your last equation, namely:
\[y - 1 + 1 = - \frac{2}{5}x + \frac{8}{5} + 1\]
furthermore, we have this:
\[\frac{8}{5} + 1 = \frac{{8 + 1 \cdot 5}}{5} = ...?\]

Answer 18

\[\frac{ 45 }{ 5 }\]

Answer 19

no, please you have to compute the multiplication first

Answer 20

Oh yeah you right, \[\frac{ 8+(1\times5) }{ 5 } =\frac{ 8+5 }{ 5 } = \frac{ 13 }{ 5 } =2 \frac{ 3 }{ 5 }\]

Answer 21

perfect! well done!

Answer 22

Why did you multiply the top by 5?

Answer 23

since the denominator of 1 is 1, so you have to add this fractions:
\[\frac{8}{5} + \frac{1}{1}\]
now the least common multiple between 5 and 1 is 5, so the denominator of your result is 5:
\[\frac{8}{5} + \frac{1}{1} = \frac{?}{5}\]
now, since 5:5= 1, then you have to multiply 8 by 1, and since 5:1=5, then you have to multiply 1 by 5, like this:
\[\frac{8}{5} + \frac{1}{1} = \frac{{\left( {8 \times 1} \right) + \left( {1 \times 5} \right)}}{5} = \frac{{8 + 5}}{5}\]

Answer 24

So i'ts kinda like you cross multiply without the equal sign in the middle then. Do you always do this for problems like these?

Answer 25

yes!

Answer 26

Okay, thank you Michele, you help me get it :)

Answer 27

thank you! :)