ccss.hsf-if.b.q.a1.dr.10 - The graph of function f passes through the coordinate points (2,3) and .(3,6). Use function notation to write the information each point gives us about function .

Sangeetha Pulapaka (last edited 2 years ago) (Expert, Educator @Qalaxia)

The equation of the line that runs through the coordinate points (2,3) and (3,6) is in the form y = mx+ b, where m is the slope of the line and b is the y-intercept.

For this we need to find the slope m, by using the slope formula m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}.

Consider x_{1} = 2, y_{1} = 3, x_{2}=3, y_{2}=6.

m = \frac{6-3}{3-2} = \frac{3}{1} = 3.

Consider (x, y) as (2, 3) and plug in m = 3 in the equation y = mx + b to get

b = 3 - 6 = -3.

So, the equation of the line passing between the two points will be y = 3x -3

We can write this in function notation form as f(x) = 3x - 3.

This gives us the information about each point on the line, for example if x = 1, then f(x) = 3 - 3 = 0.

If x = 2, f(x) = 6 - 3 = 3.