Question

What is the equation of the line which includes points (1, 3) and (2, 8)?

Answer 1

y - 3 = 5(x - 1)

Explanation:

Slope: as we move from (1, 3) to (2, 8), x increases by 1 and y increases by 5. Hence, the slope of this line is m = rise / run = 5/1, or just m = 5.

In point-slope form, the pertinent equation is

y - 3 = 5(x - 1)

Answer 2

The equation will be like this: y=ax+c. a is the slope and c is where the line crosses the (vertical) y axis - AKA the y-intercept.

As for the slope, it can be found like [(8-3)/(2-1)]. That gives 5. Another way to see it is to notice that between (1,3) and (2,8), the line moved up 5 points and went to the right only 1.

And for the y-intercept, make the equation y = 5x + c. Solve for c by filling x and y with information from any of the two points. Let's choose (1,3). Plugging in gives the equation 3=5(1)+c. C equals -2.

So, the final equation is:

y = 5x - 2