Question

(3,1) a solution of 3p-4q=13

Answer 1

3p-4q=13

Geometric figure: Straight Line

 Slope = 1.500/2.000 = 0.750

 p-intercept = 13/3 = 4.33333

 q-intercept = 13/-4 = -3.25000

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                    3*p-4*q-(13)=0

Step by step solution :

Step  1  :

Equation of a Straight Line

1.1     Solve   3p-4q-13  = 0

"y=mx+b" is the formula of a straight line drawn on Cartesian coordinate system in which "y" is the vertical axis and "x" the horizontal axis.

In this formula :

y tells us how far up the line goes

x tells us how far along

m is the Slope or Gradient i.e. how steep the line is

b is the Y-intercept i.e. where the line crosses the Y axis

The X and Y intercepts and the Slope are called the line properties. We shall now graph the line  3p-4q-13  = 0 and calculate its properties

Calculate the Y-Intercept :

Notice that when p = 0 the value of q is 13/-4 so this line "cuts" the q axis at q=-3.25000

 q-intercept = 13/-4  = -3.25000

Calculate the X-Intercept :

When q = 0 the value of p is 13/3 Our line therefore "cuts" the p axis at p= 4.33333

 p-intercept = 13/3  =  4.33333

Calculate the Slope :

Slope is defined as the change in q divided by the change in p. We note that for p=0, the value of q is -3.250 and for p=2.000, the value of q is -1.750. So, for a change of 2.000 in p (The change in p is sometimes referred to as "RUN") we get a change of -1.750 - (-3.250) = 1.500 in q. (The change in q is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

Slope     =  1.500/2.000 =  0.750

Geometric figure: Straight Line

 Slope = 1.500/2.000 = 0.750

 p-intercept = 13/3 = 4.33333

 q-intercept = 13/-4 = -3.25000