Write the function that represents the line joining the points (2,5) and (-1,3)

Question

Write the function that represents the line joining the points (2,5) and (-1,3)

Answer 1

Let's use slope-intercept form to write an equation for this line. The general form is y=mx+b, where m is the slope and b is the y-intercept (where the line crosses the y axis and x=0).

1. First, find the slope. The formula for this is (y₂-y₁)/(x₂-x₁).

We have (-1,3) and (2,5). Either one can go first, so let's choose (-1,3).

m=(3-5)/(-1-2).

In the numerator, the difference in the y-coordinates, we have 3-5 = -2.

In the denominator, the difference in the x-coordinates, we get -1-2= -3.

The slope, is m=-2/-3 = 2/3.

1. Plug the slope into the general equation along with a given ordered pair for x & y to solve for b:

I'll choose (2,5) for a point. So x=2, y=5, and m=2/3.

y=mx+b becomes 5=(2/3)2 + b

Simplify the right hand side to 5 = 4/3 +b.

Subtract 4/3 from both sides to get 11/3 = b.

1. Plug m and b into the general form equation:

y=(2/3)x + 11/3.

I hope this helps, and have fun mathing! You can do this!

LizZ