Ch. 2 - Graphs and Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 2 - Graphs and Functions

Problem 41

Chapter 3, Problem 41

Find the slope and y-intercept of each line, and graph it. x+2y = -4

Verified step by step guidance

Rewrite the given equation $ x + 2y = -4 $ in slope-intercept form $ y = mx + b $, where $ m $ is the slope and $ b $ is the y-intercept.

To isolate $ y $, subtract $ x $ from both sides: $ 2y = -x - 4 $.

Next, divide every term by 2 to solve for $ y $: $ y = \frac{-x}{2} - 2 $.

Identify the slope $ m $ as the coefficient of $ x $, which is $ -\frac{1}{2} $, and the y-intercept $ b $ as the constant term, which is $ -2 $.

To graph the line, plot the y-intercept point $ (0, -2) $ on the coordinate plane, then use the slope $ -\frac{1}{2} $ to find another point by moving down 1 unit and right 2 units from the y-intercept, and draw the line through these points.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Slope-Intercept Form of a Line

The slope-intercept form is y = mx + b, where m represents the slope and b the y-intercept. Converting an equation into this form makes it easier to identify these values directly and to graph the line.

Slope of a Line

The slope measures the steepness and direction of a line, calculated as the ratio of the change in y to the change in x (rise over run). A positive slope rises to the right, while a negative slope falls.

Y-Intercept

The y-intercept is the point where the line crosses the y-axis, occurring when x = 0. It represents the value of y at this point and is essential for graphing the line accurately.

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Graphing Intercepts

Related Practice

Textbook Question

Find the slope of the line satisfying the given conditions. through (2, -1) and (-3, -3)

Textbook Question

Find the coordinates of the other endpoint of each line segment, given its midpoint and one endpoint. See Example 5(b).

midpoint $open paren 6 a comma 6 b close paren$ , endpoint $open paren 3 a comma 5 b close paren$

Textbook Question

Graph each equation. ƒ(x) = x

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Textbook Question

Give a rule for each piecewise-defined function. Also give the domain and range.

Textbook Question

Determine whether each relation defines y as a function of x. Give the domain and range. x-y<4

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Textbook Question

Plot each point, and then plot the points that are symmetric to the given point with respect to the (a) x-axis, (b) y-axis, and (c) origin. (-4, -2)