Algebra I Finding the Rate of Change Slope

Algebra I Finding the Rate of Change (Slope) January 3, 2013

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Introduction…. . Definitions. Slope- The ratio of the vertical change to the horizontal change. Also known as the Rate of Change.

Finding Slope given Standard Form or Slope-Intercept Form Standard Form- Ax + By = C Slope-Intercept Form- y = mx + b Step 1: Solve the equation for y (if not already). Step 2: Slope is always the coefficient of x. Coefficient- The numerical factor when a term has a variable. In other words, it is the number directly beside the variable (letter). Such as 3 is the coefficient of 3 x

Finding Slope given Standard Form or Slope-Intercept Form Example: Find the slope of the following linear equation y = 6 x + 4 Step 1: Solve the equation for y. This linear equation is already solved for y because y is on one side of the equal sign by itself. Step 2: Slope is the coefficient of x. The coefficient of x in this equation is 6. Therefore, the slope of this linear equation is 6.

Finding Slope given Standard Form or Slope-Intercept Form Example: Find the slope of the following equation 15 – ⅗x = y Step 1: Solve the equation for y. This equation is already solved for y because y is on one side of the equal sign by itself. Step 2: Slope is the coefficient of x. The coefficient of x is -⅗. Therefore, the slope of this linear equation is -⅗.

Finding Slope given Standard Form or Slope-Intercept Form Example: Find the slope of the following equation 4 x – 2 y = 16 Step 1: Solve the equation for y. This equation is not already solved for y. So we need to solve this equation for y. When we do this, we will get the equation y = -8 + 2 x Step 2: Slope is the coefficient of x. The coefficient of x is 2. Therefore, the slope of this linear equation is 2.

Finding Slope given Standard Form or Slope-Intercept Form Try the following problems on your own. Find the slope of the following linear equations. 1. 2. 3. 4. 5. 4 x + 6 = y 5 - ¼x = y 2 x – 5 = y 2 y = 5 x + 3 -4 x + 2 y = 10

Finding Slope given Standard Form or Slope-Intercept Form Try the following problems on your own. Find the slope of the following linear equations. 1. 2. 3. 4. 5. 6 x + 8 y = 12 -⅓x + 3 = 5 y 6 x = 3 y + 15 Challenge: y = -3 Challenge: x = -4

Finding Slope given the graph of the line. When given the graph of a linear equation, you can pick any two points and create a right triangle connecting the two points. This is called the slope triangle. When you count the rise and run you will find the slope or the rate of change.

Finding Slope given the graph of the line.

Exit Slip! Find the slope of the line given the following equations. 1. -8 x + 2 y = 10 2. y = -2 x + 4 Find the slope of the lines graphed on the coordinate plane below. 4. 3. 3. 4.