Q57. - Algebra 2

Question

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

57. $\mathbf{y}=-\mathbf{3}\mathbf{x}+\mathbf{1}$, $\mathbf{y}=-\mathbf{x}+\mathbf{1}$, $\mathbf{y}=-\mathbf{5}\mathbf{x}+\mathbf{1}$, $\mathbf{y}=-\mathbf{7}\mathbf{x}+\mathbf{1}$

 

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, $y=-3x+1$, $y=-x+1$, $y=-5x+1$, $y=-7x+1$.

Step 3 – Calculate the slopes

Comparing the given equations with the standard slope-intercept form of equation, $y=mx+c$, the slope of $y=-3x+1$ is -3, the slope of $y=-x+1$ is -1, the slope of $y=-5x+1$ is -5 and the slope of $y=-7x+1$ is -7.

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.