Answer:
1: −5y+8x=−18
Slope = 3.200/2.000 = 1.600
x-intercept = -18/8 = -9/4 = -2.25000
y-intercept = 18/5 = 3.60000
2: Slope = -0.800/2.000 = -0.400
x-intercept = 58/2 = 29
y-intercept = 58/5 = 11.60000
Explanation:
1: Step 1 :
Equation of a Straight Line
1.1 Solve -5y+8x+18 = 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 -5y+8x+18 = 0 and calculate its properties
Graph of a Straight Line :
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 18/5 so this line "cuts" the y axis at y= 3.60000
y-intercept = 18/5 = 3.60000
Calculate the X-Intercept :
When y = 0 the value of x is -9/4 Our line therefore "cuts" the x axis at x=-2.25000
x-intercept = -18/8 = -9/4 = -2.25000
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 3.600 and for x=2.000, the value of y is 6.800. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 6.800 - 3.600 = 3.200 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
2: Same thing