Ch. 2 - Functions and Graphs

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

Blitzer 8th Edition

Ch. 2 - Functions and Graphs

Problem 72a

Chapter 3, Problem 72a

Use intercepts to graph each equation. 6x-3y+15=0

Verified step by step guidance

Rewrite the equation in standard form to make it easier to find the intercepts:

6x - 3y + 15 = 0

To find the x-intercept, set

y = 0

in the equation and solve for

x

. Substitute

y = 0

into

6x - 3y + 15 = 0

, which simplifies to

6x + 15 = 0

. Solve for

x

To find the y-intercept, set

x = 0

in the equation and solve for

y

. Substitute

x = 0

into

6x - 3y + 15 = 0

, which simplifies to

-3y + 15 = 0

. Solve for

y

Plot the x-intercept and y-intercept on the coordinate plane. The x-intercept is the point where the graph crosses the x-axis, and the y-intercept is the point where the graph crosses the y-axis.

Draw a straight line through the two intercepts to graph the equation. This line represents the solution to the equation

6x - 3y + 15 = 0

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.

Intercepts

Intercepts are points where a graph intersects the axes. The x-intercept occurs when y=0, and the y-intercept occurs when x=0. For the equation 6x - 3y + 15 = 0, finding these intercepts helps in plotting the graph accurately.

Linear Equations

A linear equation represents a straight line when graphed on a coordinate plane. The general form is Ax + By + C = 0, where A, B, and C are constants. The equation given can be rearranged to slope-intercept form (y = mx + b) to identify the slope and y-intercept.

Graphing Techniques

Graphing techniques involve methods to visually represent equations on a coordinate plane. For linear equations, plotting the intercepts and using the slope to find additional points allows for an accurate representation of the line. Understanding these techniques is essential for effective graphing.

Recommended video:

Guided course

02:16

Graphs and Coordinates - Example

Related Practice

Textbook Question

Find a. (fog) (x) b. the domain of f o g.

f(x) = x² + 4, g(x) = √(1 − x)

Textbook Question

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=-√(x + 1)

Textbook Question

Begin by graphing the square root function, f(x) = √x. Then use transformations of this graph to graph the given function. h(x)=√(-x+1)

Textbook Question

Find a. (fog) (x) b. the domain of f o g.

f(x) = √x, g(x) = x − 2

Textbook Question

Find the slope of the line passing through each pair of points or state that the slope is undefined. Assume that all variables represent positive real numbers. Then indicate whether the line through the points rises, falls, is horizontal, or is vertical. (-a, 0) and (0, -b)

Textbook Question

Use the graph of g to solve Exercises 71–76.

Find g(2)