1Cademy - Identifying the Slope and y-Intercept of $$x + 2y = 6$$

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Slope-Intercept Form of an Equation of a Line

Example

Identifying the Slope and y-Intercept of $x + 2y = 6$

When a linear equation is not already in slope-intercept form, the first step is to solve the equation for $y$ before the slope and y-intercept can be identified.

Given: $x + 2y = 6$

Step 1 — Solve for $y$ . Subtract $x$ from both sides:

$2y = -x + 6$

Divide both sides by $2$ :

$\frac{2y}{2} = \frac{-x + 6}{2}$

Split the fraction on the right using the rule $\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}$ :

$y = \frac{-x}{2} + \frac{6}{2}$

Simplify:

$y = -\frac{1}{2}x + 3$

Step 2 — Compare to the slope-intercept form $y = mx + b$ .

Step 3 — Identify the slope: The coefficient of $x$ is $-\frac{1}{2}$ , so $m = -\frac{1}{2}$ .

Step 4 — Identify the y-intercept: The constant term is $3$ , so the y-intercept is the point $(0, 3)$ .

This example illustrates that when a linear equation is given in a form other than $y = mx + b$ , solving for $y$ first is essential before the slope and y-intercept can be read from the equation.

Updated 2026-04-21

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OpenStax Elementary Algebra

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