3 Points on a Line
A line segment containing the points (13,18) and (12,8) will also contain which of the following points?Answer
Points that lie on the same line fit a line equation. Let us first determine the line equation for the 2 given points
Determine slope (m) of the line that contains (13,18) and (12,8)
| m = | y2 - y1 |
| x2 - x1 |
| m = | 8 - 18 |
| 12 - 13 |
| m = | -10 |
| -1 |
m = 10
Step 2: Determine the line equation that has a slope of containing the point (x1, y1) = (13,18)
We know that the standard line equation is y = mx + b. Rearranging that equation to solve for b, we get b = y - mx. Using the point that you entered =(13,18) and the slope (m) = 10 that you entered, let's plug in those values and evaluate:
b = 18 - (10 * 13)
b = 18 - 130
b = -112
Step 3: Form line equation
Therefore, the line equation that contains the points (13,18) and (12,8) is y = 10x - 112Plug in points to determine answer
Plugging in (19,78) as a potential answer, we get:y = 10(19) - 112
y = 190 - 112
y = 78
