Question

In Exercises 11 and 12, sketch the lines through the point with the indicated slopes on the same set of coordinate axes. Point $(2,3)$ Slopes (a) 0 (b) 1 (c) 2 (d) -3

Name: Problem 11, Chapter 1: Precalculus with Limits: A Graphing Approach
Uploaded: 2020-05-30T14:11:38-08:00
Duration: 1 min 19 s
Channel: Heather Zimmers
Description: In Exercises 11 and 12, sketch the lines through the point with the indicated slopes on the same set of coordinate axes. Point (2,3) Slopes (a) 0 (b) 1 (c) 2 (d) -3

   In Exercises 11 and 12, sketch the lines through the point with the indicated slopes on the same set of coordinate axes.
Point
$(2,3)$
Slopes
(a) 0
(b) 1
(c) 2
(d) -3

Precalculus with Limits: A Graphing Approach

Ron Larson 6th Edition

Chapter 1, Problem 11

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Solved by Expert Heather Zimmers

05/30/2020

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We need to sketch four lines that pass through the point (2,3) with different slopes: 0, 1, 2, and -3. Show more…

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In Exercises 11 and 12, sketch the lines through the point with the indicated slopes on the same set of coordinate axes. Point $(2,3)$ Slopes (a) 0 (b) 1 (c) 2 (d) -3

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Key Concepts

Slope

The slope of a line is a measure of its steepness and direction, calculated as the ratio of the vertical change to the horizontal change between any two points on the line. It is a fundamental concept in algebra and calculus that determines how fast one variable changes in relation to another.

Point-Slope Form

The point-slope form of a linear equation provides a convenient method for writing the equation of a line when a point on the line and the slope are known. It is typically expressed as y - y? = m(x - x?), where (x?, y?) is a point on the line and m is the slope.

Graphing Linear Equations on a Coordinate System

Graphing linear equations involves plotting points on a coordinate plane and drawing the straight line that passes through these points. Key elements include the use of coordinate axes, equal interval scales, and an understanding of how the slope influences the direction and steepness of the line.

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