Help with math pleaseeee
What is the y-intercept of the line with the equation 5X+y=9?
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)
Check the solution:
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 =-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)