3 Points on a Line
A line segment containing the points (4,6) and (8,10) 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 (4,6) and (8,10)
| m = | y2 - y1 |
| x2 - x1 |
| m = | 10 - 6 |
| 8 - 4 |
| m = | 4 |
| 4 |
m = 1
Step 2: Determine the line equation that has a slope of containing the point (x1, y1) = (4,6)
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 =(4,6) and the slope (m) = 1 that you entered, let's plug in those values and evaluate:
b = 6 - (1 * 4)
b = 6 - 4
b = 2
Step 3: Form line equation
Therefore, the line equation that contains the points (4,6) and (8,10) is y = 1x + 2Plug in points to determine answer
Plugging in (7,9) as a potential answer, we get:y = 1(7) + 2
y = 7 + 2
y = 9
