Question

The points (4,r) and (6,-10) lie on a line with slope -3. Find the missing coordinate r.My question: Does it matter how I use the slope formula, such as y2-y1/x2-x1?

Answer 1

r = -4

Step-by-step explanation

The formula for a slope of a line that passes through points (x1, y1) and (x2, y2) is:

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

The order of the points doesn't matter as long as you write both coordinates of the same point first (or second). The formula above is the same as:

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

With this in mind, we can find r with either of the forms of the formula:

`-3=(-10-r)/(6-4)=(r-(-10))/(4-6)`

Using the first one:

`\begin{gathered} -3=(-10-r)/(2) \\ -3\cdot2=-10-r \\ -6=-10-r \\ 10-6=-r \\ 4=-r \\ r=-4 \end{gathered}`