Linear Relationship Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
A taxi charges a \3 base fee plus \2 per mile. Write the equation for total cost \(C\) in terms of miles \(m\). Identify slope and y-intercept.

Solution

  1. 1
    Base fee (y-intercept): \(b = 3\).
  2. 2
    Cost per mile (slope): \(m_{\text{rate}} = 2\).
  3. 3
    Equation: \(C = 2m + 3\).
  4. 4
    This is in the form \(y = mx + b\) with slope 2 and y-intercept 3.

Answer

\(C = 2m + 3\); slope = 2, y-intercept = 3
A linear relationship \(y = mx + b\) has constant slope \(m\) (rate of change) and y-intercept \(b\) (starting value).

About Linear Relationship

A relationship between two variables where the rate of change is constant, producing a straight line when graphed. Expressed as y=mx+by = mx + b where mm is the slope.

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More Linear Relationship Examples

Example 2 medium

Two points on a line are ((1, 5)) and ((3, 11)). Find the equation of the line in (y = mx + b) form.

Example 3 easy

For the equation (y = 4x - 1), find (y) when (x = 3) and (x = 0).

Example 4 medium

Points ((0, -2)) and ((4, 6)) lie on a line. Find the equation in (y = mx + b) form.

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