Write the equation of the line that passes through the points (7,8) and (9,-9).

Slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
Standard form, which is ax+by=c, where a, b, and c are integer coefficients but a and b cannot be equal to 0, and a cannot be negative
Slope-point form, which is [tex]y-y_1=m(x-x_1)[/tex], where m is the slope and [tex](x_1, y_1)[/tex] is a point

The most common way is slope-intercept form, so let's write the equation of the line this way.

First, we need to find the slope of the line

The slope (m) can be found 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, which is what we need to find the equation of the line, but let's label the values of the points to avoid any confusion and mistakes

[tex]x_1=7\\y_1=8\\x_2=9\\y_2=-9[/tex]

Now substitute into the formula

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

m=[tex]\frac{-9-8}{9-7}[/tex]

Subtract

m=[tex]\frac{-17}{2}[/tex]

The slope of the line is -17/2

Now substitute this as m in y=mx+b:

y = -17/2x + b

Now we need to find b

As the line passes through both (7,8) and (9,-9), we can use either point to help solve for b

Taking (9, -9) for example:

Substitute 9 as x and -9 as y in the equation

-9 = -17/2(9) + b

Multiply

-9 = -76.5 + b

Add -76.5 to both sides

135/2 = b

Substitute 135/2 as b into the equation

y = -17/2x + 135/2

Hope this helps!

Topic: Finding the equation of the line

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