Constant Rate Math Example 2

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Example 2

medium
Find the equation of the line passing through (2,5)(2, 5) and (6,13)(6, 13), interpret the slope, and write it in slope-intercept form y=mx+by = mx + b.

Solution

  1. 1
    Compute slope: m=13−56−2=84=2m = \frac{13-5}{6-2} = \frac{8}{4} = 2.
  2. 2
    Use point-slope form with (2,5)(2, 5): y−5=2(x−2)⇒y=2x−4+5=2x+1y - 5 = 2(x - 2) \Rightarrow y = 2x - 4 + 5 = 2x + 1.
  3. 3
    Interpret: the rate of change is m=2m=2, meaning yy increases by 22 for every 11-unit increase in xx.

Answer

y=2x+1y = 2x + 1; slope m=2m = 2
Slope measures constant rate of change. Given two points, compute rise over run to find mm. The yy-intercept bb is the output when x=0x=0, found by substituting a known point.

About Constant Rate

A constant rate of change means the output increases (or decreases) by the same fixed amount for every unit increase in the input — the hallmark of a linear function.

Learn more about Constant Rate →

More Constant Rate Examples

Example 1 easy

A car travels at a constant speed of [formula] km/h. Write the distance function [formula], find [fo

Example 3 easy

A plumber charges a [formula]50[formula][formula] per hour. Write [formula] and find the cost for [f

Example 4 medium

Determine whether the data is consistent with a constant rate of change: [formula] and [formula]. If

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