1. Refer to the equation 3x − 4y = 12. (a) Create a table of values for at least 4 points. Show your work on how you found the values for each coordinate pair, and validated the points were on the line.

Accepted Solution

Answer:   The table of values is attached. The graph of the line shows that the points [tex](-1,-3.75), (0,-3), (1, -2.25)\ and\ (2,-1.5)[/tex] lie on the line. Step-by-step explanation: The equation of the line in Slope-Intercept form is: [tex]y=mx+b[/tex] Where "m" is the slope and "b" is the y-intercept. Given the equation:  [tex]3x-4y = 12[/tex] We can solve for the variable "y" in order to write in Slope-Intercept form: [tex]3x-4y = 12\\\\-4y=-3x+12\\\\y=\frac{3}{4}x-3[/tex]The nex step is to give values to the variables "x", then substitute each value into  the equation and evaluate, in order to find the correspondings values of "y". [tex]For\=-1:\\\\y=\frac{3}{4}(-1)-3=-3.75[/tex] [tex]For\ x=0:\\\\y=\frac{3}{4}(0)-3=-3[/tex] [tex]For\ x=1:\\\\y=\frac{3}{4}(1)-3=-2.25[/tex] [tex]For\ x=2:\\\\y=\frac{3}{4}(2)-3=-1.5[/tex] With this values we can make the table attached.  We can identify the slope of the line and the y-intercept are: [tex]m=\frac{3}{4}\\\\b=-3[/tex] Then we can graph it Observe that the points [tex](-1,-3.75), (0,-3), (1, -2.25)\ and\ (2,-1.5)[/tex] lie on the line.