Linear Functions Math Example 2

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Example 2

medium
Find the equation of the line through (1,3)(1, 3) and (4,12)(4, 12).

Solution

  1. 1
    Find the slope: m=12−34−1=93=3m = \frac{12 - 3}{4 - 1} = \frac{9}{3} = 3.
  2. 2
    Use point-slope form with (1,3)(1, 3): y−3=3(x−1)y - 3 = 3(x - 1).
  3. 3
    Expand: y−3=3x−3y - 3 = 3x - 3, so y=3xy = 3x.

Answer

y=3xy = 3x
To find the equation of a line from two points, first compute the slope, then use point-slope form y−y1=m(x−x1)y - y_1 = m(x - x_1) and simplify.

About Linear Functions

A function whose graph is a straight line, characterized by a constant rate of change between any two points.

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More Linear Functions Examples

Example 1 easy

Write the equation of a line with slope [formula] and [formula]-intercept [formula].

Example 3 medium

Write the equation of a line with slope [formula] that passes through [formula].

Example 4 easy

What are the slope and [formula]-intercept of [formula]?

Example 5 hard

Convert [formula] to slope-intercept form.

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