Which graph represents the solution of the inequality -5x + 4y = 16?

Slope = 2.500/2.000 = 1.250

 x-intercept = 16/-5 = -3.20000

 y-intercept = 16/4 = 4

Step-by-step explanation:

Step  1  :

Pulling out like terms :

1.1     Pull out like factors :

  -5x + 4y - 16  =   -1 • (5x - 4y + 16)

Equation at the end of step  1  :

Step  2  :

Equation of a Straight Line

2.1     Solve   -5x+4y-16  = 0

Tiger recognizes that we have here an equation of a straight line. Such an equation is usually written y=mx+b ("y=mx+c" in the UK).

"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  -5x+4y-16  = 0 and calculate its properties

Graph of a Straight Line :

 Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 4/1 so this line "cuts" the y axis at y= 4.00000

 y-intercept = 16/4  =  4

Calculate the X-Intercept :

When y = 0 the value of x is 16/-5 Our line therefore "cuts" the x axis at x=-3.20000

 x-intercept = 16/-5  = -3.20000

Calculate the Slope :

Slope is defined as the change in y divided by the change in x. We note that for x=0, the value of y is 4.000 and for x=2.000, the value of y is 6.500. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 6.500 - 4.000 = 2.500 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     =  2.500/2.000 =  1.250

Geometric figure: Straight Line

 Slope = 2.500/2.000 = 1.250

 x-intercept = 16/-5 = -3.20000

 y-intercept = 16/4 = 4

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