Linear Relationship Math Example 2

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

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.

Solution

  1. 1
    Slope: \(m = \frac{11-5}{3-1} = \frac{6}{2} = 3\).
  2. 2
    Use point-slope with \((1, 5)\): \(5 = 3(1) + b \Rightarrow b = 2\).
  3. 3
    Equation: \(y = 3x + 2\).
  4. 4
    Check with \((3,11)\): \(3(3)+2 = 11\) ✓

Answer

\(y = 3x + 2\)
Find slope using \(m = \Delta y / \Delta x\), then solve for \(b\) using one point. The equation \(y = 3x + 2\) satisfies both points.

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 1 easy

A taxi charges a [formula]2 per mile. Write the equation for total cost (C) in terms of miles (m). I

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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