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Chapter 2: Q56. (page 74)

Use a graphing calculator to investigate each family of graphs. Explain how changing the slope affects the graph of the line.

56. y=2x+3, y=4x+3, y=8x+3, y=x+3

Short Answer

Expert verified

It is determined that changing the slope rotates the line about its y-intercept.

Step by step solution

01

– State the concept

The slope intercept form of a straight-line equation is y=mx+c where mis the slope andc is the y-intercept.

02

– List the given data

The given equations, y=2x+3, y=4x+3, y=8x+3, y=x+3.

03

– Calculate the slopes

Comparing the given equations with y=mx+c, the slope of y=2x+3 is 2, the slope of y=4x+3 is 4, the slope of y=8x+3 is 8 and the slope of y=x+3 is 1.

04

– Graphing the equations

Graphing the given equations, we have,

Graphical Interpretation

From the graph of the given equations, it is clear that changing the slope rotates the line about its y-intercept.

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