Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

2. Graphs of Equations

Lines

College Algebra

2. Graphs of Equations

Lines

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2:03 minutes

Problem 2

Textbook Question

Fill in the blank(s) to correctly complete each sentence. The graph of the line y= -2x+7 has slope and y-intercept .

Verified step by step guidance

Identify the slope-intercept form of a linear equation, which is \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Compare the given equation \( y = -2x + 7 \) with the slope-intercept form \( y = mx + b \).

Recognize that the coefficient of \( x \) in the equation \( y = -2x + 7 \) is \( -2 \), which represents the slope \( m \).

Identify that the constant term in the equation \( y = -2x + 7 \) is \( 7 \), which represents the y-intercept \( b \).

Fill in the blanks: The graph of the line \( y = -2x + 7 \) has slope \( -2 \) and y-intercept \( 7 \).

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Key Concepts

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

Slope

The slope of a line in a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In the equation y = mx + b, 'm' denotes the slope. A positive slope indicates that as x increases, y also increases, while a negative slope indicates that y decreases as x increases. For the equation y = -2x + 7, the slope is -2.

Y-Intercept

The y-intercept of a line is the point where the line crosses the y-axis, which occurs when x equals zero. In the slope-intercept form of a linear equation, y = mx + b, 'b' represents the y-intercept. This value indicates the starting point of the line on the y-axis. For the equation y = -2x + 7, the y-intercept is 7, meaning the line crosses the y-axis at the point (0, 7).

Linear Equation

A linear equation is an algebraic equation that represents a straight line when graphed on a coordinate plane. It is typically expressed in the form y = mx + b, where 'm' is the slope and 'b' is the y-intercept. Linear equations can model relationships with constant rates of change, making them fundamental in algebra. The equation y = -2x + 7 is a specific example of a linear equation.