Q56. - Algebra 2

Question

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

56. $\mathbf{y}=\mathbf{2}\mathbf{x}+\mathbf{3}$, $\mathbf{y}=\mathbf{4}\mathbf{x}+\mathbf{3}$, $\mathbf{y}=\mathbf{8}\mathbf{x}+\mathbf{3}$, $\mathbf{y}=\mathbf{x}+\mathbf{3}$

Step-by-Step Solution

Answer

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

Step 1 – State the concept

The slope intercept form of a straight-line equation is $y=mx+c$ where m is the slope and c is the y-intercept.

Step 2 – List the given data

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

Step 3 – 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.

Step 4 – 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.