Linear functions

Linear functions are the most common function type on the SAT. They show up as equations, tables, graphs, and word problems — often all in one question.

The core idea is simple: the output changes at a constant rate. If a gym charges $30 per month plus a $50 sign-up fee, the total cost is 𝐶 =30𝑚 +50. The slope (30) tells you how fast the cost grows; the y-intercept (50) tells you where it starts.

Most SAT linear-function questions test whether you can move fluidly between representations — read a slope from a table, match an equation to a graph, or pull the right numbers from a word problem into 𝑦 =𝑚𝑥 +𝑏. The algebra is usually straightforward; the challenge is translating context into math and back.

Get comfortable with slope-intercept form 𝑦 =𝑚𝑥 +𝑏, point-slope form 𝑦 −𝑦1 =𝑚(𝑥 −𝑥1), and function notation 𝑓(𝑥). Know what each piece means in a real-world scenario, and you'll handle these questions quickly.