Question

If A(2;2) and B(-3;4), determine the equation of AB, in the form y=mx+c​

Answer 1

Answer:

$y = -\frac{2}{5}x + \frac{14}{5}$

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + c$

In which m is the slope and c is the y-intercept(value of y when x = 0).

A(2;2) and B(-3;4)

When we have two points, the slope is the change in y divided by the change in x. So

Change in y: 4 - 2 = 2

Change in x: -3 - 2 = -5

Slope: $m = \frac{2}{-5} = -\frac{2}{5}$

So

$y = -\frac{2}{5}x + c$

A(2;2)

When $x = 2, y = 2$. We use this to find c.

$y = -\frac{2}{5}x + c$

$2 = -\frac{2}{5}(2) + c$

$c = 2 + \frac{4}{5} = \frac{10}{5} + \frac{4}{5} = \frac{14}{5}$

So

$y = -\frac{2}{5}x + \frac{14}{5}$