Question

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.

Answer 1

Answer:  

The table of values is attached.

The graph of the line shows that the points $(-1,-3.75), (0,-3), (1, -2.25)\ and\ (2,-1.5)$ lie on the line.

Step-by-step explanation:

The equation of the line in Slope-Intercept form is:

$y=mx+b$

Where "m" is the slope and "b" is the y-intercept.

Given the equation:

 $3x-4y = 12$

We can solve for the variable "y" in order to write in Slope-Intercept form:

$3x-4y = 12\\\\-4y=-3x+12\\\\y=\frac{3}{4}x-3$

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".

$For\=-1:\\\\y=\frac{3}{4}(-1)-3=-3.75$

$For\ x=0:\\\\y=\frac{3}{4}(0)-3=-3$

$For\ x=1:\\\\y=\frac{3}{4}(1)-3=-2.25$

$For\ x=2:\\\\y=\frac{3}{4}(2)-3=-1.5$

With this values we can make the table attached.

 We can identify the slope of the line and the y-intercept are:

$m=\frac{3}{4}\\\\b=-3$

Then we can graph it

Observe that the points $(-1,-3.75), (0,-3), (1, -2.25)\ and\ (2,-1.5)$ lie on the line.