9. Finding the Slope

3 ways to find the slope (m) of a line

1. Count "rise over run" 2. Use the equation for the line. 3. Calculate with the slope formula.

1st way to find the slope: "rise over run"

1. Find a point on the line (x,y). 2. Find the next closest coordinate. 3. Count the number of spaces vertically between the points (the y). This is the "rise." 4. Count the spaces horizontally between the points (the x). This is the "run" 5. Write "rise" over the "run" as a fraction: rise −− run This is the slope! 6. Write the negative sign on your fraction if the slope is negative (downhill).

Practice: Finding slope with rise over run

1. Pick one point. Let's go with (2,2). 2. Pick another point. Let's choose (1,1). 3. Count spaces between the points up and down. There is 1 space between them. Our rise is 1. 4. Count spaces between them left and right. There is 1 space between them. Our run is 1. 5. Write rise over run. Our rise over run is 1/1. So, 1/1 is our slope!

3rd Way to Find Slope: "Slope of the Line" Formula

1. Take two points (they will either give them to you or you pick two points from the graph). Label one point Point 1 and the other Point 2. - the x of Point 1 will be x₁ and the y of Point 1 will b y₁ - the x of Point 2 will be x₂ and the y of Point 1 will b y₂ 2. To find the slope, plug these values into the slope equation: m = (y₂ - y₁) ÷ (x₂ - x₁) 3. Use your calculator to find the number on the top and the number on the bottom. 4. The answer to the formula is the slope!

What is the slope of a line that is parallel to the x-axis (a horizontal line)?

A line that is parallel to the x-axis has a slope of m = 0.

What is the slope of a line parallel to the y-axis (a vertical line)?

A line that is parallel to the y-axis has a slope of m = undefined.

Practice: Finding the Slope Using the Equation 16 + 4y = 4x

First, get "y" alone. 4y = 4x - 16 Divide everything by 4: y = 1x + 4 Since our equation is y = mx + b m = 1, so our slope is 1

2nd Way to Find Slope: Using the Equation of the Line

If the problem doesn't have a graph, you can find the slope right there in the equation! Linear equations are written in the form y = mx + b. The slope is m. For example, if you have: y = 4x + 2 the "m" is 4 so the slope is 4! *if the equation isn't in this form, use your algebra skills to move everything into the right place*

Are left-tilting slopes positive or negative?

Left-tilting (downhill) slopes are negative. How do you know which way it's tilting? Start by looking at the lowest point on the line, then go up to the highest point to see which way the line is tilting. It counts even if the line is tilting a tiny bit.

Practice: Using the Slope Formula Find the slope of a line with these two points: Point 1: (-3,2) Point 2: (4,1)

Point 1: (-3,2) and Point 2: (4,1) x₁ = -3 y₁ = 2 x₂ = 4 y₂ = 1 m = (y₂ - y₁) ÷ (x₂ - x₁) m = (1 - 2) ÷ (4 - -3) m = (-1) ÷ (7) So, m = -1/7

Practice: Using the Slope Formula Find the slope of a line with these two points: Point 1: (8,-5) Point 2: (-5,7)

Point 1: (8,-5) and Point 2: (-5,7) x₁ = 8 y₁ = -5 x₂ = -5 y₂ = 7 m = (y₂ - y₁) ÷ (x₂ - x₁) m = (7 - -5) ÷ (-5 - 8) m = (12) ÷ (-13) So, m = 12/-13

Are right-tilting slopes positive or negative?

Right-tilting (uphill) slopes are positive. How do you know which way it's tilting? Start by looking at the lowest point on the line, then go up to the highest point to see which way the line is tilting. It counts even if the line is tilting a tiny bit.

What is slope?

The "slope" of a line is a number that describes how tilted the line is. Linear equations represent it with "m".

Practice: Finding the Slope Using the Equation y = -6x + 1

y = -6x + 1 y = mx + b m = -6 So, the slope is -6.