Question

Write an equation of the line that passes through the points (1, 1) and (7, 4).

A) y = 2x - 10
B) y = 2x - 1
C) y = (1/2)x + 5
D) y = (1/2)x + 1/2
Please help I am so confused

Answer 1

First, find the slope of the line.

\(\LARGE \color{black}{ \displaystyle {\rm m}=\frac{\color{blue}{{\rm y}_1}-\color{red}{{\rm y}_2}}{\color{green}{{\rm x}_1}-\color{darkgoldenrod}{{\rm x}_2}} }\)



where

\(\LARGE \color{black}{ \displaystyle {\rm m} }\) is the slope

\(\Large\color{black}{ \displaystyle (\color{green}{{\rm x}_1}~,~~\color{blue}{{\rm y}_1}) }\) and \(\Large\color{black}{ \displaystyle (\color{darkgoldenrod}{{\rm x}_2}~,~~\color{red}{{\rm y}_2}) }\) are you points.

Answer 2

in your case

\(\LARGE \color{black}{ \displaystyle {\rm m}=\frac{\color{blue}{1}-\color{red}{4}}{\color{green}{1}-\color{darkgoldenrod}{7}} }\)

Answer 3

what would your slope (m) be?

Answer 4

3/6 or 1/2

Answer 5

yes, that is correct, m=1/2

Answer 6

Now you can use the point slope form to find the equation of the line.

\(\large\color{black}{ \displaystyle {\rm y}-\color{purple}{{\rm y}_1} ={\rm m}\left({\rm x-\color{purple}{{\rm x}_1}}\right) }\)

Answer 7

you can use any of the points, lets choose (1,1)

\(\large\color{black}{ \displaystyle {\rm y}-\color{purple}{1} =\frac{1}{2}\left({\rm x-\color{purple}{1}}\right) }\)

Answer 8

now, all you need is to simplify this expression.

Answer 9

I am a little confused still sorry

Answer 10

what exactly confuses u?

Answer 11

well, as it is now it is also fine in a point slope form.
However to make it one of your options you need a y-intercept form.

Answer 12

\(\large\color{black}{ \displaystyle {\rm y}-\color{purple}{1} =\frac{1}{2}\left({\rm x-\color{purple}{1}}\right) }\)

\(\large\color{black}{ \displaystyle {\rm y}-\color{purple}{1} =\frac{1}{2}{\rm x}-\frac{1}{2}}\)

Answer 13

then, add 1 to both sides, and you get?

Answer 14

I understand the y- 1 + 1/2x = 1/2 but I am confused when I add 1 to each side

Answer 15

\(\large\color{black}{ \displaystyle {\rm y}-1 =\frac{1}{2}{\rm x}-\frac{1}{2}}\)

\(\large\color{black}{ \displaystyle {\rm y}-1\color{red}{+1} =\frac{1}{2}{\rm x}-\frac{1}{2}\color{red}{+1} }\)

\(\large\color{black}{ \displaystyle {\rm y} =\frac{1}{2}{\rm x}+\frac{1}{2}}\)

Answer 16

Now it makes better sense. I am sorry Thank you for the break down to help me understand it better