Find the slop of 3x + 7y = 20 ?
Answers
STEP
1
:
Equation of a Straight Line
1.1 Solve 3x-7y-20 = 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 3x-7y-20 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 20/-7 so this line "cuts" the y axis at y=-2.85714
y-intercept = 20/-7 = -2.85714
Calculate the X-Intercept :
When y = 0 the value of x is 20/3 Our line therefore "cuts" the x axis at x= 6.66667
x-intercept = 20/3 = 6.66667
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 -2.857 and for x=2.000, the value of y is -2.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -2.000 - (-2.857) = 0.857 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 0.857/2.000 = 0.429
Geometric figure: Straight Line
Slope = 0.857/2.000 = 0.429
x-intercept = 20/3 = 6.66667
y-intercept = 20/-7 = -2.85714