**Middle School Number Sense Lesson 67: Finding the Intercept of a Line or Function**

And now it is time for another quick geometry lesson... By definition, the

**intercept**of a a line is the coordinate of the point at which it crosses one of the axes.

- The
**x-intercept**is the point where the line crosses the**x-axis**(where**y = 0**). - The
**y-intercept**is the point where the line crosses the**y-axis**(where**x = 0**).

**11 times**last year, with a median placement at

**question # 67**.

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You may be asked to find the intercept of a line or function in a few different ways:

- Given an equation
- Given two points
- Given an equation (missing a constant or coefficient) and the other intercept
- Given an equation of a line parallel or perpendicular to the one in question

**Definitions:**

- The
**abscissa**of a coordinate is the**x-value**of the ordered pair. For example, the abscissa of (1, 2) is**1**. - The
**ordinate**of a coordinate is the**y-value**of the ordered pair. For example, the ordinate of (1, 2) is**2**. *The easiest way for me to remember which is which, is that they appear in alphabetical order.***Abscissa**comes before**ordinate**, and**x**comes before**y**.

**Example 1: If (a, b) is the y-intercept of the line 5x - 6y = 30, then b = ___**

- Since we are looking for the y-intercept, set
**x equal to 0**. **5(0) - 6y = 30**becomes**-6y = 30**.- Divide both sides by
**-6**, and you have y =**-5**.

**Example 2: The x-intercept of 3x - 2y = 24 is ___**

- The x-intercept means
**y = 0**. **3x - 2(0) = 24**becomes**3x = 24**.- Divide both sides by
**3**, and you have x =**8**.

**Example 3: The abscissa of the x-intercept of the line y = .5x + 10 is ___**

- The x-intercept means
**y = 0**. **0 = .5x + 10**. Subtract 10 from both sides to get**-10 = .5x**- Divide both sides by
**.5**to get**-20****= x**.

**Example 4: The ordinate of the y-intercept of the line 5y - 5x = -20 is ___**

- The y-intercept means
**x = 0**. **5y - 5(0) = -20**becomes**5y = -20**.- Divide both sides by
**5**to get**y = -4**.

**Example 5: If the y-intercept of 4x + 3y = C is 8, then the x-intercept is ___**

- The y-intercept means
**x = 0**. Solve for C: 4(0) + 3(8) = C. 0 + 24 = C, so C =**24**. - The x-intercept means
**y = 0**. Solve for x: 4x + 3(0) = 24. 4x = 24, so x =**6**.

**Example 6: If the x-intercept of 4x - 5y = k is (5, 0), then the ordinate of the y-intercept is ___**

- The x-intercept means
**y = 0**. Solve for k: 4(5) - 5(0) = k. 20 - 0 = k, so k =**20**. - The y-intercept means
**x = 0**. Solve for y: 4(0) - 5y = 20. -5y = 20, so y =**-4**.

**Example 7:**

**The y-intercept of f(x) = 2(x - 3)**

^{2}+ 1 is ___1. The y-intercept means

**x = 0**.

2. f(x) = 2(0 - 3)

^{2}+ 1 = 2(-3)

^{2}+ 1 = 2(9) + 1 = 18 + 1 =

**19**.

**Check back soon for a free worksheet to help you practice FindIntercept.**

**Up Next for Middle School: AddSquareDoub**