Skip to main content
Ch. 2 - Graphs and Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 2 - Graphs and FunctionsProblem 56
Chapter 3, Problem 56

For each line, (a) find the slope and (b) sketch the graph. 4x + 3y = 12

Verified step by step guidance
1
Rewrite the given equation \(4x + 3y = 12\) in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. To do this, solve for \(y\): subtract \(4x\) from both sides to get \(3y = -4x + 12\).
Divide every term by 3 to isolate \(y\): \(y = \frac{-4}{3}x + 4\). Now the equation is in the form \(y = mx + b\), where the slope \(m = -\frac{4}{3}\) and the y-intercept \(b = 4\).
Identify the slope \(m = -\frac{4}{3}\). This means for every 3 units you move to the right along the x-axis, the line goes down 4 units along the y-axis.
To sketch the graph, start by plotting the y-intercept point \((0, 4)\) on the coordinate plane.
From the y-intercept, use the slope to find another point: move 3 units to the right (positive x-direction) and 4 units down (negative y-direction), then plot this second point. Draw a straight line through these two points to complete the graph.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
6m
Was this helpful?

Key Concepts

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

Slope of a Line

The slope measures the steepness of a line and is calculated as the ratio of the change in y to the change in x (rise over run). For a line in standard form Ax + By = C, the slope is found by rearranging to slope-intercept form y = mx + b, where m is the slope.
Recommended video:
Guided course
06:49
The Slope of a Line

Converting Standard Form to Slope-Intercept Form

To find the slope easily, rewrite the equation from standard form (Ax + By = C) to slope-intercept form (y = mx + b) by isolating y. This process involves solving for y, which reveals the slope (m) and y-intercept (b) directly.
Recommended video:
04:34
Converting Standard Form to Vertex Form

Graphing a Linear Equation

Graphing involves plotting points that satisfy the equation and drawing a line through them. Using the slope and y-intercept, you can start at the y-intercept on the graph and use the slope to find another point, then draw the line through these points.
Recommended video:
06:00
Categorizing Linear Equations
Related Practice
Textbook Question

Graph each function. Give the domain and range. g(x)=[[2x-1]]

9
views
Textbook Question

Let ƒ(x)=2x-3 and g(x)=-x+3. Find each function value. See Example 5.

(ƒ∘g)(4)(ƒ∘g)(4)

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. g(1/2)

1
views
Textbook Question

Write an equation (a) in standard form and (b) in slope-intercept form for each line described. through (-2, -2), parallel to y=3

Textbook Question

Let ƒ(x)=-3x+4 and g(x)=-x2+4x+1. Find each of the following. Simplify if necessary. ƒ(-7/3)

1
views
Textbook Question

Determine whether each function is even, odd, or neither. ƒ(x)=-x3+2x

1
views