suppose f is a linear function where f(3) = 4 and f(8) = 4. What kind of line is the graph of f?

Answer 1

The first important thing this question tells us it that f is linear. This means that it always looks like a straight line with no curves or breaks. It could be horizontal or angled, but it will always be a straight line so now we have to figure out what the angle, or slope, is.

They give us two values for the function: f(3) = 4, and f(8) = 4. This tells us that the points (3,4) and (8,4) are on our line. The equation for the slope of a line can be written as:

(y₂ - y₁)/(x₂ - x₁)

In our problem (x₁,y₁) = (3,4), and (x2,y2) = (8,4), so:

(y₂ - y₁)/(x₂ - x₁) = (4 - 4)/(8-3) = 0/5 = 0

A line with 0 slope is a horizontal line.