Which properties justify the steps taken to solve the system?
4x + 3y = 25
2x +-5y = 19
Drag the answers into the boxes to match each step.

Slope = -2.667/2.000 = -1.333

 x-intercept = 25/4 = 6.25000

 y-intercept = 25/3 = 8.33333

Step-by-step explanation:

Step  1  :

Equation of a Straight Line

1.1     Solve   4x+3y-25  = 0

I recognize 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  4x+3y-25  = 0 and calculate its properties

Graph of a Straight Line :

Calculate the Y-Intercept :

Notice that when x = 0 the value of y is 25/3 so this line "cuts" the y axis at y= 8.33333

 y-intercept = 25/3  =  8.33333

Calculate the X-Intercept :

When y = 0 the value of x is 25/4 Our line therefore "cuts" the x axis at x= 6.25000

 x-intercept = 25/4  =  6.25000

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 8.333 and for x=2.000, the value of y is 5.667. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.667 - 8.333 = -2.667 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)

   Slope     = -2.667/2.000 = -1.333

Geometric figure: Straight Line

 Slope = -2.667/2.000 = -1.333

 x-intercept = 25/4 = 6.25000

 y-intercept = 25/3 = 8.33333

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