Linear functions show up everywhere: prices, distance, growth, and more. Once you understand slope and intercepts, you can solve and graph them quickly.
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Solve Now →A linear function is a function whose graph is a straight line. The most common form is y = mx + b.
If your task is to solve a linear equation in one variable (like 3x + 5 = 14), start with how to solve linear equations step by step. Linear functions often use the same algebra, but they add interpretation (slope, intercepts, and graphs).
Substitute an x-value and compute the output.
Set the function equal to a given output and solve for x.
If you already have y = mx + b, then:
Standard form is Ax + By = C. You can find intercepts quickly:
Example: 3x + 2y = 12
If you want to practice converting to y = mx + b, the next guide focuses on that: how to solve slope intercept form.
A gym charges $20 to join and $15 per month.
Let x = months and y = total cost. The join fee is a starting amount, so it’s the intercept.
Question: How many months until the cost reaches $110?
Interpretation: after 6 months, the total cost is $110.
In y = mx + b, m is attached to x. b is the constant. If there’s no x, it’s not slope.
When you move terms, remember you’re adding/subtracting the same amount on both sides.
In word problems, define x and y. The same equation can mean different things in different contexts.
For functions, you might be asked to evaluate f(3), find intercepts, or interpret slope.
If you’d like a few more graph-and-slope examples in the same style, Khan Academy’s linear equations & graphs unit is a good reference.
Paste your linear function and get slope, intercepts, and solutions.
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