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 [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] where ([tex]x_1[/tex],[tex]y_1[/tex]) and ([tex]x_2[/tex],[tex]y_2[/tex]) are points

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

[tex]x_1[/tex]=5/7

[tex]y_1[/tex]=4

[tex]x_2[/tex]=-5/7

[tex]y_2[/tex]=3

Now substitute into the formula

m=[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

m=[tex]\frac{3-4}{\frac{-5}{7}-\frac{5}{7}}[/tex]

Subtract and simplify

m=[tex]\frac{-1}{\frac{-10}{7}}[/tex]

m=-1*[tex]\frac{7}{-10}[/tex]

m=[tex]\frac{-7}{-10}[/tex]

m=[tex]\frac{7}{10}[/tex]

So the slope of the line is [tex]\frac{7}{10}[/tex]

Here is the equation of the line so far:

y=[tex]\frac{7}{10}x[/tex]+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=[tex]\frac{7}{10}[/tex]*[tex]\frac{5}{7}[/tex]+b

Multiply and simplify the fractions

4=[tex]\frac{1}{2}[/tex]+b

subtract 1/2 from both sides

[tex]\frac{7}{2}[/tex]=b

So the equation of the line is y=[tex]\frac{7}{10}x[/tex]+[tex]\frac{7}{2}[/tex]

Hope this helps!