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 y-2x-1 = 0 and calculate its properties
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.
y-intercept = 1/1 = 1.
Calculate the X-Intercept :
When y = 0 the value of x is 1/-2 Our line therefore "cuts" the x axis at x=-0.5
x-intercept = 1/-2 = -0.5
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 1.000 and for x=2.000, the value of y is 5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.000 - 1.000 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Answers & Comments
Answer:
Slope = 4./2. = 2.
x-intercept = 1/-2 = -0.5
y-intercept = 1/1 = 1.
Explanation:
Solve y-2x-1 = 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 y-2x-1 = 0 and calculate its properties
Calculate the Y-Intercept :
Notice that when x = 0 the value of y is 1/1 so this line "cuts" the y axis at y= 1.
y-intercept = 1/1 = 1.
Calculate the X-Intercept :
When y = 0 the value of x is 1/-2 Our line therefore "cuts" the x axis at x=-0.5
x-intercept = 1/-2 = -0.5
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 1.000 and for x=2.000, the value of y is 5.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of 5.000 - 1.000 = 4.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
Slope = 4/2 = 2.