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

Verified step by step guidance

1. Identify the given equation: \$11x + 2y = 3$.
2. Rewrite the equation in slope-intercept form \(y = mx + b\), where \(m\) represents the slope.
3. Isolate \(y\) by subtracting \$11x\( from both sides: \)2y = -11x + 3$.
4. Divide every term by 2 to solve for \(y\): \(y = \frac{-11}{2}x + \frac{3}{2}\).
5. Identify the slope \(m\) as the coefficient of \(x\), which is \(-\frac{11}{2}\).

Key Concepts

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.