Graph the line that passes through the points ( 2 , 5 ) and ( − 1 , − 4 ) and determine the equation of the line.

Answer 1

To find the equation, first find the slope. The slope (also known as "m") is calculated from the slope equation:

where the points are (x₂, y₂) and (x₁, y₁) in other words x₁ = 2, y₁ = 5, x₂ = -1, and y₂ = -4

so m = (-4 - 5)/(-1 - 2) = -9/-3 = 3.

The generic form of a line is y = mx + b and you only need to fill in the "m" and the "b". You now know what the "m" is (3). So the equation with the "m" filled in is y = 3x + b. To determine "b", use one of the points as the value of "x" and "y" in the equation. So, how about us picking (2, 5) so plugging in x = 2 and y = 5 into y = 3x + b gives us:

5 = 3(2) + b

5 = 6 + b

-1 = b

Now plug that value for "b" back into the equation y = 3x + b to get y = 3x - 1