What is an equation of the line that passes through the points (5, 5) and (-5, -7)?

There are 3 ways to write the equation of the line, but the most common way is slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept

So, first we need to find the slope

The slope can be calculated from 2 points using the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex], where [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] are points

We have 2 points, but let's label their values to avoid any confusion when calculating.

[tex]x_1=5\\y_1=5\\x_2=-5\\y_2=-7[/tex]

Now substitute these values into the formula.

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

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

Subtract

m=[tex]\frac{-12}{-10}[/tex]

Simplify

m=[tex]\frac{6}{5}[/tex]

The slope of the line is 6/5

We can substitute that as m in y=mx+b

Here is the equation of the line so far:

y=6/5x+b

Now we need to find b

As the equation passes through the points (5, 5) and (-5, -7), we can use either one of them to help solve for b

Using (5,5) for example:
5=6/5(5)+b

Multiply

5=6+b

Subtract 6 from both sides

-1=b

Substitute -1 as b:

y= 6/5x - 1

Hope this helps!

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