Answer:
Slope = -1.500/2.000 = -0.750
a-intercept = 6/3 = 2
b-intercept = 6/4 = 3/2 = 1.50000
Step-by-step explanation:
Step 1 :
Equation of a Straight Line
1.1 Solve 3a+4b-6 = 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 3a+4b-6 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when a = 0 the value of b is 3/2 so this line "cuts" the b axis at b= 1.50000
b-intercept = 6/4 = 3/2 = 1.50000
Calculate the X-Intercept :
When b = 0 the value of a is 2/1 Our line therefore "cuts" the a axis at a= 2.00000
a-intercept = 6/3 = 2
Calculate the Slope :
Slope is defined as the change in b divided by the change in a. We note that for a=0, the value of b is 1.500 and for a=2.000, the value of b is -0.000. So, for a change of 2.000 in a (The change in a is sometimes referred to as "RUN") we get a change of -0.000 - 1.500 = -1.500 in b. (The change in b 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
a-intercept = 6/3 = 2
b-intercept = 6/4 = 3/2 = 1.50000
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