Answer:A unique line is defined by any two distinct (not identical) points. You have two distinct, which means you have a line. To find the equation for the line, we start with the slope-intercept equation for a line. This is only a template for a generic line, so we will have to find the specific values of m (slope) and b (y-intercept) that define your line.
The template: y = mx + b
b is the y-intercept, which, if you look at (0,–2), you will see is –2; it is where the line crosses the y-axis. Fill that value of b into our template to get:
y = mx – 2
Now, we only need the value of m, which is the slope. If you have two points on a line, you can calculate the slope of that line. The slope is the change (difference) of y over the change in x (difference) of x for two given points on the line. It's a fraction or ratio though sometimes it can be reduced to an integer.
So, taking your two points, you calculate the slope, m, in the following way:
(x1,y1) = (0,–2)
(x2,y2) = (5,1)
y2 – y1 1 – (–2) 1 + 2 3
m = ________ = ________ = ________ = ____
x2 – x1 5 — 0
Explanation: