Graph the following equation

Question

Graph the following equation and show all work. 

 

y=-4x+1

Answer 1

This equation  (y = -4x + 1) is in the form (y = mx + b), where m is the slope and b is the point where the line crosses the y-axis.

 

The slope (m) is a value that tells us how fast the line increases or decreases.  Since this equation has a value for m = -4, it is decreasing (the negative value).  We commonly call this rise over the run. 

 

The y-intercept value (b) = +1.

Hence the plot is :  (apologies for not being able to do graphics here !) contact me and I'll send you an email with a more detailed plot.

 

        Y

 

        |

     \  |

      \ |

       \|

        \   +1

        |\

        | \

------+--\--------------------------------   X

        |    \

        |     \

        |      \

        |       \

 

 

 

 

 

 

 

 

 

 

Answer 2

The equation y= -4x + 1 is in the "slope-intercept" form of y=mx+b, where m is the slope (rise over run), and b is the y-intercept (where the line will cross the vertical y-axis).

 

You need graph paper for an accurate graph (but it's possible to do it on notebook paper).

 

It's best to start at the y-intercept and plot your first point there. Put a dot on the y-axis 1 unit up from the origin.

 

I like to rewrite the slope as a fraction, to better visualize the "rise over run" so -4 becomes -4/1. This means I rise negative 4 (fall 4) and run to the right 1.

 

So, starting at the dot you made at the y-intercept, count down 4 units, then right 1 unit, and draw your second dot. You can repeat the process starting there for more points: count down 4, then right 1.

 

Lastly, you can go back to the y-intercept and count in the opposite direction, since your slope is also equal to positive 4 over negative 1. You can then count UP 4 units, and LEFT 1 unit.

Answer 3

y=-4x+1 is in the form y=mx+b where m is the slope and b is the y-intercept

the slope is -4 or (-4/1) or (4/-1) and the line crosses the y-axis at 1

 

plot the point (0,1)

from this point move 4 units down and 1 unit to the right to come to the point (1,-3), now plot this point

from the point (0,1) move 4 units up and 1 unit to the left to come to the point (-1,5), now plot this point

the slope is defined as the rise over the run (rise/run)

rise means up or down on the y-axis and run means left or right on the x-axis

you have three points: (0,1), (1.-3), and (-1,5); connect these points with a ruler and you have the graph

 

Answer 4

Hi Theresa;

I am assuming that you know how to graph.  If not, please let me know.

What you are going to do is calculate the value of y for a list of values of x.

It would be most logical to do this...

 

 x| y

-2|

-1|

 0|

 1|

 2|

 

y=-4x+1

y=-4(-2)+1=8+1=9

 

y=-4x+1

y=-4(-1)+1=4+1=5

 

y=-4(0)+1=1

 

y=-4x+1

y=-4(1)+1=-4+1=-3

 

y=-4(2)+1=-8+1=-7

 

x | y
-2|9
-1|5
 0|1
 1|-3
 2|-7