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Find the x- and y-intercepts of the graph of 10x+2y=20 State each answer as an integer or an improper fraction in simplest form.

Sagot :

Answer:

  • Slope: [tex]\frac{10.000}{2.000} = -5.000[/tex]
  • x - intercept: [tex]\frac{10}{5} = 2[/tex].
  • y intercept: [tex]\frac{10}{1} = 10.00000[/tex].

Step-by-step explanation:

Simplify:

  • Simplify the equation by subtracting what is to the right of the equal sign from both sides of the equation:
  • 10*x+2*y-(20)=0.

Step 1:

  • Pull out like factors:
  • 10x + 2y - 20 = 2 * (5x + y - 10)

Step 2:

  • Equations which are never true:
  • Solve:
  • 2 = 0
  • This can't be solved.
  • A non-zero constant never equals 0.
  • Equation of a straight line:
  • Solve:  5x+y-10 = 0
  • "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  5x+y-10  = 0 and calculate its properties
  • Calculate the y-intercept:
  • Notice that when x = 0 the value of y is 10/1 so this line "cuts" the y axis at y=10.00000
  •  y-intercept = 10/1  = 10.00000
  • Calculate the x-intercept:
  • 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 10.000 and for x=2.000, the value of y is -0.000. So, for a change of 2.000 in x (The change in x is sometimes referred to as "RUN") we get a change of -0.000 - 10.000 = -10.000 in y. (The change in y is sometimes referred to as "RISE" and the Slope is m = RISE / RUN)
  •    Slope     = -10.000/2.000 = -5.000

Answers:

  •  Slope = -10.000/2.000 = -5.000
  •  x-intercept = 10/5 = 2
  •  y-intercept = 10/1 = 10.00000
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