Ch. 2 - Functions and Graphs

Blitzer8th EditionCollege AlgebraISBN: 9780136970514Not the one you use?Change textbook

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 41

Chapter 3, Problem 41

In Exercises 41–44, use the given conditions to write an equation for each line in point-slope form and slope-intercept form. Passing through (-3, 2) with slope - 6

Verified step by step guidance

Identify the point-slope form of a linear equation, which is given by:

y - y_1 = m(x - x_1)

, where

m

is the slope and

(x_1, y_1)

is a point on the line.

Substitute the given slope

m = -6

and the point

(x_1, y_1) = (-3, 2)

into the point-slope form. This gives:

y - 2 = -6(x - (-3))

Simplify the equation from step 2 to get the point-slope form:

y - 2 = -6(x + 3)

To convert to slope-intercept form, expand the equation from step 3. Distribute

-6

across

(x + 3)

, resulting in:

y - 2 = -6x - 18

Solve for

y

by adding

2

to both sides of the equation:

y = -6x - 16

. This is the slope-intercept form of the equation.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.

Video duration:

Was this helpful?

Key Concepts

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

Point-Slope Form

Point-slope form is a way to express the equation of a line given a point on the line and its slope. The formula is written as y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. This form is particularly useful for quickly writing the equation of a line when you know a specific point and the slope.

Slope-Intercept Form

Slope-intercept form is another way to express the equation of a line, defined as y = mx + b, where m is the slope and b is the y-intercept. This form is beneficial for easily identifying the slope and where the line crosses the y-axis. Converting from point-slope to slope-intercept form allows for a clearer understanding of the line's behavior.

Slope

The slope of a line measures its steepness and direction, calculated as the change in y over the change in x (rise over run). A positive slope indicates the line rises as it moves from left to right, while a negative slope indicates it falls. In this question, the slope is given as -6, meaning for every unit increase in x, y decreases by 6 units, which is crucial for forming the line's equation.

Recommended video:

Guided course

05:17

Types of Slope

Related Practice

Textbook Question

Use the graph of y = f(x) to graph each function g. g(x) = -½ ƒ ( x + 2) - 2

602

views

Textbook Question

Find f/g and determine the domain for each function. f(x) = √x, g(x) = x − 4

1111

views

Textbook Question

Give the center and radius of the circle described by the equation and graph each equation. Use the graph to identify the relation's domain and range. x² + y² = 16

867

views

Textbook Question

Find fg and determine the domain for each function. f(x) = √x, g(x) = x − 4

1181

views

Textbook Question

Find $f+g$ , $f-g$ , $fg$ , and $\frac{f}{g}$ . Determine the domain for each function.

$f$\left$(x$\right$)=$\sqrt{x}$$ , $g$\left$(x$\right$)=x-5$

717

views

Textbook Question

In Exercises 39–48, give the slope and y-intercept of each line whose equation is given. Then graph the linear function. f(x) = -2x+1

132

views