Question

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.

Answer 1

Answer:

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

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