Question

Find the equation in standard form, of a line passing through (3, -4) and (5,1).
a. 5x+2y=23
b. y=5/2x-23/2
c. 5x-2y=23
d. 2y-3y=9

I feel like the answer is in between A and C .... I'm leaning on C.

Answer 1

use the general equation of the straight line
\[\frac{ y-y _{1} }{ x-x _{1} }=\frac{ y _{2} -y _{1}}{ x _{2}-x _{1} }\]

Answer 2

okay, I got, -5/2 as the slope.
then, I used point-slope form and got the equation y-(-4)=-5/2(x-3)
so, I now have y= -5/2x-7

Answer 3

Standard form is Ax+By=C with no fractions.
It looks like you have the slope correct, but you did not multiply the -5/2 but the -3 when you simplified your equation

Answer 4

Try the slope 1 more time...

1 - (-4) 1 + 4 5
------- = ------- = ---- Positive slope not negative
5 - 3 5 - 3 2

Answer 5

So it would be A?

Answer 6

Then by using the point (5,1) we have

\[\large y - 1 = \frac{5}{2}(x - 5)\]
\[\large y - 1 = \frac{5}{2}x - \frac{25}{2}\]
\[\large y = \frac{5}{2}x - \frac{23}{2}\]

This is slope intercept form...how would you make this standard form?

Answer 7

*Hint..No fractions...

Answer 8

multiplying? the denominators? or finding a way to cancel out 2.

Answer 9

Well by multiplying each term by 2 you essentially cancel the 2...

\[\large (2y = \frac{5}{\cancel{2}}x - \frac{23}{\cancel{2}})\times \cancel{2} \]
\[\large 2y = 5x - 23\]

Now what?

Remember Standard form is in the form Ax + By = C