−14x+21y=84 draw on the graph
Answers
Step-by-step explanation:
Step by Step Solution:
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Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
-14*x-21*y-(84)=0
STEP
1
:
Pulling out like terms
1.1 Pull out like factors :
-14x - 21y - 84 = -7 • (2x + 3y + 12)
Equation at the end of step
1
:
STEP
2
:
Equations which are never true
2.1 Solve : -7 = 0
This equation has no solution.
A a non-zero constant never equals zero.
Equation of a Straight Line
2.2 Solve 2x+3y+12 = 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+3y+12 = 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 = -12/3 = -4
Calculate the X-Intercept :
When y = 0 the value of x is -6/1 Our line therefore "cuts" the x axis at x=-6.00000
x-intercept = -12/2 = -6
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 -5.333. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -5.333 - (-4.000) = -1.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = -1.333/2.000 = -0.667
Geometric figure: Straight Line
Slope = -1.333/2.000 = -0.667
x-intercept = -12/2 = -6
y-intercept = -12/3 = -