If a system of linear equations has infinitely many solutions, then the graph of the system is:
1 answer:
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Answer:
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
2*x-y-(4)=0
Step 1:
Equation of a Straight Line
Solve 2x-y-4 = 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 2x-y-4 = 0 and calculate its properties
Graph of a Straight Line :
( see attatchment)
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 = 4/-1 = -4.00000
Calculate the X-Intercept :
When y = 0 the value of x is 2/1 Our line therefore "cuts" the x axis at x= 2.00000
x-intercept = 4/2 = 2
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 0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 0.000 - (-4.000) = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2
Geometric figure: Straight Line
1. Slope = 2
2. x-intercept = 4/2 = 2
3. y-intercept = 4/-1 = -4.00000
- clarification for graph - green means rise red means run , bottom black is x intercept which is 2.000 under rise is y-intercept and under the y axis is 0.000 and -4.000.
