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What is the y-intercept of the line with the equation 5X+y=9?

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2 Answers

Solution: (0,9) is the y-intercept point of the line 5x+y=9 To understand why, please read the following step by step solution.

STEP 1: Read, understand the situation within, identify and pull out important information.

  • The equation of the line is given in the standard form: Ax + By = C, where “A” (5) is a positive integer, “B” (1) and “C” (9) are integers.
  • The standard form equation is very useful to determine the y-intercept point and the x-intercept point, using the same methodology.
  • The y-intercept point is the point where a line crosses the y-axis (coordinate x=0).
  • The coordinates of any point of the given line must satisfy the equation 5x+y=9. So, if we substitute the coordinates of any point of the line on its equation, we must get an identity!

STEP 2: Translate keywords to their mathematical symbols:

  • The y-intercept point is given by (0,y). These coordinates must be a solution of the equation 5x+y=9. Therefore,
  • 5(0) + y = 9           by substituting the coordinates of the point (0,y)

STEP 3: Set up and solve the equation or problem:

5(0) + y = 9
           y = 9                So, the y-intercept point is (0,9)

STEP 4: Check the solution:
   5x+y=9            
5(0)+9=9        by substituting the coordinates of the y-intercept point (0,9)
        9 = 9       It’s an identity. Our point (0,9) is the y-intercept point of the line 5x+y=9

STEP 5: Curiosities

  • Using the same methodology we can get the x-intercept point (9/5,0) or (1.8,0)
  • Graphing the line in a standard form equation: plot the two intercepts points (9/5,0) and (0,9), one is lying on the x-axis, and the other on the y-axis, and draw a line through these two points. Easy, isn’t?

5x+y=9

-5x  =-5x. Subtract -5x from both sides

y=-5x+9. Put in slope intercept form y=mx+b

y=-5(0)+9. Look for yup intercept by plugging in 0 for x

y=9     Solve. Y=9.  Writing as an ordered pair is. (0,9)

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