Geometric figure: Straight Line
Slope = 2.333/2.000 = 1.167
x-intercept = -15/7 = -2.14286
y-intercept = 15/6 = 5/2 = 2.50000
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
7*x-6*y-(-15)=0
Step by step solution :
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Step 1 :
Equation of a Straight Line
1.1 Solve 7x-6y+15 = 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 7x-6y+15 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 5/2 so this line "cuts" the y axis at y= 2.50000
y-intercept = 15/6 = 5/2 = 2.50000
Calculate the X-Intercept :
When y = 0 the value of x is -15/7 Our line therefore "cuts" the x axis at x=-2.14286
x-intercept = -15/7 = -2.14286
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 2.500 and for x=2.000, the value of y is 4.833. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 4.833 - 2.500 = 2.333 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 2.333/2.000 = 1.167
Geometric figure: Straight Line
Slope = 2.333/2.000 = 1.167
x-intercept = -15/7 = -2.14286
y-intercept = 15/6 = 5/2 = 2.50000