Before you read

Answer first — see what you already know.

A line crosses the y-axis at $(0, - 2)$ and goes upward from left to right. Which equation could represent this line?

A
$y = 3 x - 2$
B
$y = - 3 x - 2$
C
$y = 3 x + 2$
D
$y = - 3 x + 2$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

A line passes through the origin and through the point $(3, - 6)$ . What is its equation?

A
$y = 2 x$
B
$y = - 2 x$
C
$y = - \frac{1}{2} x$
D
$y = 3 x - 6$

Check your answer

Answer:

Theory

Matching an Equation to a Graph

To match a linear equation to its graph, check two things:

1. Y-intercept: Where does the line cross the y-axis? This gives you $b$ .
2. Slope: Is the line going up or down? How steep is it? This gives you $m$ .

Quick checks:
- Positive slope $\to$ line goes up ↗
- Negative slope $\to$ line goes down ↘
- Steep line $\to$ $|m| > 1$
- Gentle line $\to$ $|m| < 1$
- $m = 0$ $\to$ horizontal line
- $b > 0$ $\to$ crosses y-axis above origin
- $b < 0$ $\to$ crosses y-axis below origin
- $b = 0$ $\to$ passes through origin

Identity function f(x) = x

Constant function f(x) = 3

Theory

Key Features from a Graph

Given a graph, you can read:

Feature	How to find it
Y-intercept	Where the line crosses the y-axis
X-intercept	Where the line crosses the x-axis
Slope	Pick two clear points, use $m = \frac{\text{rise}}{\text{run}}$
Equation	Combine slope + y-intercept: $y = mx + b$
$f(a)$	Find $x = a$ on the x-axis, go to the line, read $y$
Solve $f(x) = k$	Find $y = k$ , go to the line, read $x$

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