Parameter Math Example 3

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

Example 3

medium
In the family of lines y=mx+3y = mx + 3, find the slope when the line passes through (2,7)(2, 7).

Solution

  1. 1
    Step 1: Substitute the point (2,7)(2, 7) into y=mx+3y = mx + 3: 7=m(2)+37 = m(2) + 3.
  2. 2
    Step 2: Solve for the parameter mm: 7=2m+37 = 2m + 3, so 2m=42m = 4.
  3. 3
    Step 3: Divide both sides by 2: m=2m = 2.
  4. 4
    Check: y=2(2)+3=7y = 2(2) + 3 = 7 ✓

Answer

m=2m = 2
The parameter mm determines which specific line in the family y=mx+3y = mx + 3 we have. Substituting a known point pins down the parameter value.

About Parameter

A parameter is a quantity in a mathematical expression that remains constant for a particular case but can change between cases. For example, in y = mx + b, the slope m and intercept b are parameters — each choice of m and b gives a different line.

Learn more about Parameter →

More Parameter Examples

Example 1 medium

In the family of lines [formula], what role does [formula] play?

Example 2 hard

For what value of the parameter [formula] does [formula] have the solution [formula]?

Example 4 easy

In [formula], is [formula] a variable or a parameter?

Example 5 medium

The quadratic [formula] has a zero at [formula]. Find [formula].

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