A coordinate plane with both its $x$x- and $y$y-axes ranging from $-6$−6 to $6$6. Both axes are marked at $1$1 unit intervals. Two lines, $g\left(x\right)=x+4$g(x)=x+4 and $f\left(x\right)=x$f(x)=x, which are parallel to each other are plotted on the coordinate plane. The line labeled $g\left(x\right)$g(x) is outlined in black. The line labeled $f\left(x\right)$f(x) is outlined in gray. The line $g\left(x\right)=x+4$g(x)=x+4 slopes upward and passes through $\left(0,4\right)$(0,4) and $\left(1,5\right)$(1,5). The line $f\left(x\right)=x$f(x)=x slopes upward and passes through $\left(0,0\right)$(0,0) and $\left(1,1\right)$(1,1). The points are not plotted, and their coordinates are not explicitly labeled nor given.

Is $g\left(x\right)=x+4$g(x)=x+4 steeper, less steep, or equally steep as $f\left(x\right)=x$f(x)=x?

Steeper

Less steep

Equally steep

Easy

< 1 min

The lines $g\left(x\right)=\frac{1}{3}x$g(x)=13x and $f\left(x\right)=x$f(x)=x are shown on the same coordinate plane.

Easy

< 1 min

Use the applet to help answer the question.

Easy

< 1 min

Use the applet to help answer the question.

Easy

< 1 min

Outcomes

A.F.1

The student will investigate, analyze, and compare linear functions algebraically and graphically, and model linear relationships.

A.F.1b

Investigate and explain how transformations to the parent function y = x affect the rate of change (slope) and the y-intercept of a linear function.

A.F.1f

Graph a linear function in two variables, with and without the use of technology, including those that can represent contextual situations.

A.F.1h

Compare and contrast the characteristics of linear functions represented algebraically, graphically, in tables, and in contextual situations.

3.02 Transformations of linear functions

Interactive practice questions

Outcomes

A.F.1

A.F.1b

A.F.1f

A.F.1h

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