Question

Find the equation of the line containing the points (5/7,4) and (-5/7,3)

Answer 1

y=
`(7)/(10)x+(7)/(2)`

Explanation:

Hi there!

We want to find the equation of the line containing the points (5/7,4) and (-5/7, 3)

The most common way to write an equation of the line is slope-intercept form, which is given as y=mx+b where m is the slope and b is the y intercept

So first, let's find the slope of the line

The formula for the slope calculated from two points is
`(y_2-y_1)/(x_2-x_1)` where (
`x_1`,
`y_1`) and (
`x_2`,
`y_2`) are points

We have everything needed to find the slope, but let's label the values of the points to avoid any confusion

`x_1`=5/7

`y_1`=4

`x_2`=-5/7

`y_2`=3

Now substitute into the formula

m=
`(y_2-y_1)/(x_2-x_1)`

m=
`(3-4)/((-5)/(7)-(5)/(7))`

Subtract and simplify

m=
`(-1)/((-10)/(7))`

m=-1*
`(7)/(-10)`

m=
`(-7)/(-10)`

m=
`(7)/(10)`

So the slope of the line is
`(7)/(10)`

Here is the equation of the line so far:

y=
`(7)/(10)x`+b

We need to find b

As the equation of the line passes through both (5/7, 4) and (-5/7, 3), we can use either one of them to solve for b

Let's take (5/7, 4) for this case

Substitute x as 5/7 and y as 4

4=
`(7)/(10)`*
`(5)/(7)`+b

Multiply and simplify the fractions

4=
`(1)/(2)`+b

subtract 1/2 from both sides

`(7)/(2)`=b

So the equation of the line is y=
`(7)/(10)x`+
`(7)/(2)`

Hope this helps!