1. ## Analytic Geometry Q6

Question:
Using slopes, determine if the points lie on a straight line.
a) $\displaystyle (-1,-4)$ , $\displaystyle (3,8)$ & $\displaystyle (0,-1)$
b) $\displaystyle (0,5)$ , $\displaystyle (-1,3)$ & $\displaystyle (-3,2)$

Attempt:

a) $\displaystyle (-1,-4)$ & $\displaystyle (3,8)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-(-4)}{3-(-1)} = \frac{12}{4} = 3$

$\displaystyle (3,8)$ & $\displaystyle (0,-1)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-1-8}{0-3} = \frac{-9}{-3} = 3$

It is a straight line as the slopes are the same.

b) $\displaystyle (0,5)$ & $\displaystyle (-1,3)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-5}{-1-0} = 2$

$\displaystyle (-3,2)$ & $\displaystyle (-1,3)$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-2}{(-1)-3} = \frac{1}{-4} = -\frac{1}{4}$

It is not a straight line as the slopes don't match.

2. a) you data is (0,1) but you made the calculation with (0,-1)

b) your calculation of the second slope is not correct

3. a) I have corrected the question. Is my answer right?

b) $\displaystyle (-3,2)$ & $\displaystyle (-1,3)$

$\displaystyle \color{red}{m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3-2}{(-1)-3} = \frac{1}{-4} = -\frac{1}{4}}$

$\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{2-3}{-3-1} = \frac{1}{4}$

It is still not a straight line, am I right?

4. a) OK

b) The slope is still not correct ...