Before you read

Answer first — see what you already know.

What is the y-intercept of $5 x + 2 y = 20$ ?

A
$4$
B
$10$
C
$20$
D
$5$

Check your answer

Answer:

Before you read

Answer first — see what you already know.

What is the x-intercept of $3 x - 6 y = 18$ ?

A
$(6, 0)$
B
$(18, 0)$
C
$(3, 0)$
D
$(- 3, 0)$

Check your answer

Answer:

Theory

What Is Standard Form?

Standard form of a linear equation is:
$Ax + By = C$
where $A$ , $B$ , and $C$ are constants (usually integers), and by convention $A \geq 0$ .

Advantages of standard form:
- Easy to find both intercepts
- Natural form for many word problems
- Used in systems of equations (elimination method)

Finding intercepts:
- X-intercept: set $y = 0$ , solve for $x$ $\to$ point $(\frac{C}{A}, 0)$
- Y-intercept: set $x = 0$ , solve for $y$ $\to$ point $(0, \frac{C}{B})$

3x + 2y = 6: x-intercept (2,0), y-intercept (0,3)

Example 1

Find the x- and y-intercepts of $3x + 4y = 12$ .

X-intercept ( $y = 0$ ): $3x = 12$ $\to$ $x = 4$ $\to$ point $(4, 0)$

Y-intercept ( $x = 0$ ): $4y = 12$ $\to$ $y = 3$ $\to$ point $(0, 3)$

X-intercept:

(4, 0)

, Y-intercept:

(0, 3)

Example 2

Convert $3x + 4y = 12$ to slope-intercept form.

Solve for $y$ :

$4y = -3x + 12$

$y = -\frac{3}{4}x + 3$

y = -\frac{3}{4}x + 3

Theory

Converting to Standard Form

To convert from slope-intercept to standard form:
1. Move the $x$ -term to the left side
2. If needed, multiply to clear fractions
3. Make sure $A$ is positive

Example 1

Convert $y = \frac{2}{3}x - 4$ to standard form.

Move $x$ -term: $-\frac{2}{3}x + y = -4$

Multiply by $-3$ to clear fractions and make $A$ positive:

$2x - 3y = 12$

2x - 3y = 12

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