Find the slope of each line, provided that it has a slope. 11x + 2y = 3

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Identify the given equation: $11x + 2y = 3$.

Rewrite the equation in slope-intercept form $y = mx + b$, where $m$ represents the slope.

Isolate $y$ by subtracting \$11x$ from both sides: $2y = -11x + 3$.

Divide every term by 2 to solve for $y$: $y = \frac{-11}{2}x + \frac{3}{2}$.

Identify the slope $m$ as the coefficient of $x$, which is $-\frac{11}{2}$.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Slope of a Line

The slope of a line measures its steepness and direction, defined as the ratio of the change in y to the change in x (rise over run). It indicates how much y changes for a unit change in x and is usually denoted by 'm'.

Standard Form of a Linear Equation

A linear equation in standard form is written as Ax + By = C, where A, B, and C are constants. Understanding this form is essential because it can be rearranged to slope-intercept form to easily identify the slope.

Converting to Slope-Intercept Form

To find the slope from the standard form, rearrange the equation into slope-intercept form y = mx + b, where m is the slope. This involves isolating y on one side to express the equation explicitly in terms of x.