Question 2.5.2: Using the Point-Slope Form (Given Two Points) Write an equat...
Using the Point-Slope Form (Given Two Points)
Write an equation of the line through the points (-3, 2) and (2, -4). Write the result in standard form Ax + By = C.
Find the slope first.
m = \frac{-4 – 2}{2 – (-3)} = – \frac{6}{5} Definition of slope
The slope m is – \frac{6}{5} . Either the point (-3, 2) or the point (2, -4) can be used for (x_{1} , y_{1} ). We choose (-3, 2).
y – y_{1} = m(x – x_{1} ) Point-slope form
y – 2 = – \frac{6}{5} [x – (-3)] x_{1} = -3, y_{1} = 2, m = – \frac{6}{5}
5(y – 2) = -6(x + 3) Multiply by 5.
5y – 10 = -6x – 18 Distributive property
6x + 5y = -8 Standard form
Verify that we obtain the same equation if we use (2, -4) instead of (-3, 2) in the point-slope form.