Question

Indicate in standard form the equation of the line passing through the given points.

S(1/2, 1), T(1/2, 4)

Answer 1

First find the slope from those two points.

Slope \(\Large m = \frac{y_2-y_1}{x_2-x_1}\)

Answer 2

not sure how to do that with the 1/2

Answer 3

Treat it like 0.5 (that is what it is)

Answer 4

If you are not using a calculator, you can multiply the whole fraction by 2/2. That gets rid of the halves, and multiplying by 1 won't change anything.

Answer 5

Well, in this case, the x value happens to be the same for both points.
Therefore, there is no need to even calculate slope.
If x value is the same it means the line is a vertical line, parallel to the y-axis.

(If y value is the same it means the line is a horizontal line, parallel to the x-axis.)

Answer 6

-2x + y = 0 is this right

Answer 7

Also, if slope is infinity it means the line is a vertical line.

Answer 8

No. As @aum points out, you cannot figure slope using the two points because \(x_1 - x_0 = 0\) and division by zero is a no, no.

Answer 9

The equation for a vertical line is x = constant (you will have to find the constant).
In this case x is always 1/2.

Therefore, the equation of the line is x = 1/2

Answer 10

thank you I hope I get this soon its hard

Answer 11

It will get easier with practice.

Answer 12

can you please help with one more

Answer 13

go ahead

Answer 14

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

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

Answer 15

The point-slope form of a line is: \(\Large y-y_1 = m(x-x_1)\)
where m is the slope and \(x_1 = 5, y_1 = -2\)

Answer 16

so how do I do that then I am so lost

Answer 17

\(\Large y-y_1 = m(x-x_1)\)
Put \(\Large m = \frac 25, x_1 = 5, y_1 = -2\) in the above equation.
Simplify.
Then rearrange it to put it in the standard form.

Answer 18

this is hard not having no fun thank you I will keep tring to get it with this I am sure I will sooner or later thank you so much for helping :)

Answer 19

y - y1 = m(x - x1)
m = 2/5, x1 = 5, y1 = -2
y - (-2) = 2/5 * (x - 5)
y + 2 = 2/5 * (x - 5)
To get rid of the fraction on the right multiply both sides by 5:
5y + 10 = 2 * (x-5)
5y + 10 = 2x - 10
subtract 10 from both sides
5y = 2x - 20
Put this in standard form which is Ax + By = C
subtract 5y from both sides:
0 = 2x - 5y - 20
add 20 to both sides:
20 = 2x - 5y
or
2x - 5y = 20