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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 2: Q. 16 (page 126)

Find the slope-intercept form of the equation of the line containing the points $(- 2, 4), (6, 8)$ .

Short Answer

Expert verified

The slope-intercept form is $y = \frac{1}{2} x + 5$ .

Step by step solution

01

Step 1. Given information.

Consider the given question,

$(- 2, 4), (6, 8)$

Slope of the formula,

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$

Substitute the values,

$m = \frac{8 - 4}{6 - (- 2)} = \frac{4}{8} = \frac{1}{2}$

02

Step 2. Find the point-slope form.

We know the point-slope form,

$y - y_{1} = m (x - x_{1})$

Substitute the values,

$y - 8 = \frac{1}{2} (x - 6) y - 8 = \frac{1}{2} x - 3 y = \frac{1}{2} x - 3 + 8 y = \frac{1}{2} x + 5$

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Most popular questions from this chapter

True or False

The graph of $y = - f (x)$ is the reflection about the $x$ -axis of the graph of $y = f (x)$ .

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.
$h (x) = \frac{x}{x^{2} - 1}$

If $(1, 3)$ is a point on the graph of $y = f (x)$ , which of the following points must be on the graph of $y = 2 f (x)$ ?

In March $2011$ , Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge $- \(13.55$

Distribution charge

First $20$ therms $- 0.1473 / t h e r m$

Next $30$ therm $- \) 0.0579 / t h e r m$

Over $50$ therm $- \(0.0519 / t h e r m$

Gas supply charge $- \) 0.51 / t h e r m$

(a) What is the charge for using $40$ therms in a month?

(b) What is the charge for using $150$ therms in a month?

(c) Develop a model that gives the monthly charge $C$ for $x$ therms of gas.

(d) Graph the function found in part (c).

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

$g (x) = 4 \sqrt{x}$

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