Algebra 1 > Notes > Yorkcounty Final > Yorkcounty > Lesson 20 - Slope

Lesson 20 Slope

Slope Slope is a term that describes the steepness of a line.

The line has a positive slope.

Finding the slope of a line Slope is defined as the rise of the line over the run of the line. rise Slope = run Between two points on the graph the rise was 3 and the run was 2. Slope = 3/2 When you go up the rise is positive, when you go down the rise is negative. When you run to the right it is positive and when you run to the left that is negative.

When finding the slope it helps to pick an integer value to start from. Try to pick a point that falls on two integers, (0,5) , and try to avoid picking points that do not, (1.4, 4.2) It will make finding the slope much easier.

Start with the point (0,5) and see how you get to the point (2,4)

Two get from one point to the other we went down 1 and right two; thus our slope is -1/2

Types of Slope This line has a positive slope

This line has a negative slope

This line has undefined slope

This line has zero slope

Undefined Slope Why does a vertical line has undefined slope?? Slope = rise/run

A vertical line will rise but it does not run any, thus run = 0. Slope of a vertical line = rise / 0 Remember you cannot divide by zero, that gives you an undefined statement. Thus the slope of a vertical line is undefined. Slope of a vertical line = undefined

Zero Slope Well then why does a horizontal line have a slope of zero? Slope = rise / run A horizontal line does not rise at all, thus rise = 0. Slope = 0/run ; whenever you have a zero on top of a fraction that fraction always equals zero. So the slope of a horizontal line will always equal zero. Slope of a horizontal line = 0

Try These What kind of slope does each line have?

next slide for answer…

Try These What kind of slope does each line negative have? undefined

zero

positive

negative

Try This – What is the slope of the line??

Try This – What is the slope of the line?? Down 3 Right 4

rise / run

-3/4 Slope of –3/4

This line is going down towards the right, so it has a negative slope. Notice our slope was –3/4 , a negative slope.

Slope-Intercept Form y = mx + b This is called slope intercept form. M is the variable for slope B is the variable for y-intercept

We need to be able to look at a graph and write the equation of the line. There are two steps to this process. You have to find M and B.

Slope-Intercept Form y = mx + b

STEP 1) Find B - remember B is your y-intercept. Where does the graph cross the yaxis?? It crosses at y = 5, thus 5 is your yintercept. B = 5 STEP 2) Find the slope. Down 3, Right 4. Slope is –3/4 M = -3/4 y-intercept equals 5 so B = 5 slope equals –3/4 so M = -3/4 Now substitute those values into the equation. y = mx +b now becomes y = (-3/4)x + 5

Slope-Intercept Form y = mx + b m = slope b = y-intercept To write the equation of the line by looking at the graph first find b (yintercept) and second find m (slope) After you have found b and m, substitute the values into the equation y = mx + b