Textbook Question
For each line described, write an equation in (a) slope-intercept form, if possible, and (b) standard form. through (3, -5), parallel to y = 4
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2. Graphs of Equations
Lines
0:51 minutesProblem 53
Textbook Question
Find the slope of each line, provided that it has a slope. 11x + 2y = 3
Verified step by step guidance1
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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Video duration:
51sKey Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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'.
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The Slope of a Line
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.
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05:39Standard Form of Line Equations
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.
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