1. Submitted to - Sh.Bharat Bhushan Sir Submitted by- Mayank Devnani
SEMINAR P.P.T…..
Topic- Slope-intercept form and
Equation of a line
Submitted to - Sh.Bharat Bhushan Sir
Submitted by- Mayank Devnani

2. Equation of a LINE

3. Given the Slope and Y-Intercept
Just plug them into y = mx + b
Example: Write the equation for the line with slope m = 3/2 and y-intercept b = -1

4. Given a Graph Find the slope and y-intercept.
Then, plug into y = mx + b
Example:
Write an equation of
the line shown.

5. Point-Slope Form y – y1 = m(x – x1) Used when you are given:
The slope and a point
Two points
A parallel or perpendicular line and a point

6. Parallel and Perpendicular Lines
For parallel lines:
use the same slope
For perpendicular lines:
use the opposite reciprocal (flip it and change the sign)
Then use Point-Slope form

7. Linear equations

8. Linear Equations Vocabulary 1) linear equation 2) linear function
3) standard form
4) y-intercept
5) x-intercept

9. Linear Equations Sara has 4 hours after dinner to study and dox 6 4 -2 2
Sara has 4 hours after dinner to study and do
homework. She has brought home algebra 2
and chemistry.
If she spends x hours on algebra and y hours on chemistry, a portion of the graph
of the equation x + y = 4 can be used to
relate how much time she spends on each.
An equation such as x + y = 4 is called a linear equation.

10. x has an exponent other than 1.
Linear Equations
A linear function is a function whose ordered pairs satisfy a linear equation.
Any linear function can be written in the form f(x) = mx + b, where m and b
are real numbers.
State whether each function is a linear function. Explain.
a) f(x) = 10 – 5x
Yes!
It can be written as f(x) = – 5x + 10
m = – 5, b = 10
b) g(x) = x4 – 5
No!
x has an exponent other than 1.
c) h(x, y) = 2xy
No!
Two variables are multiplied together.

11. Linear Equations Standard Form of a Linear Function
The standard form of a linear function is Ax + By = C,
where A > 0,
A and B are not both zero.
Also, A, B, and C are integers whose greatest common factor is 1
Write the equation in Standard Form:

12. Linear Equations
In the previous lesson, you graphed functions by using a table of values.
Since two points determine a line, there are quicker ways to graph linear functions.
One way is to find the points at which the graph intersects each axis and then connect
them with a line. y x
The y-coordinate of the point at which the graph
crosses the y-axis is called the ____________.
(0, 3)
y - intercept
(-4, 0)
The x-coordinate of the point at which the graph
crosses the x-axis is called the ____________.
x - intercept

13. Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.
Then graph the equation.
The x-intercept is the value of x when y = 0. y x
(0, 5)
(3, 0)
The y-intercept is the value of y when x = 0.

14. Slope-Intercept Form

15. FORMULA FOR FINDING SLOPE
The formula is used when you know two points of a line.

16. Find the slope of the line between the two points (-4, 8) and (10, -4)
If it helps label the points.
Then use the formula

17. Graphing Linear Equations
In Slope-Intercept Form

18. We have already seen that linear equations have two variables and when we plot all the (x,y) pairs that make the equation true we get a line.
In this section, instead of making a table, evaluating y for each x, plotting the points and making a line, we will use The Slope-Intercept Form of the equation to graph the line.

19. Notice that these equations are all solved for y.
These equations are all in Slope-Intercept Form:
Notice that these equations are all solved for y.

20. Just by looking at an equation in this form, we can draw the line (no tables).
The constant is the y-intercept.
The coefficient is the slope.
Constant = 1, y-intercept = 1.
Coefficient = 2, slope = 2.
Constant = -4, y-intercept = -4.
Coefficient = -1, slope = -1.
Constant = -2, y-intercept = -2.
Coefficient = 3/2, slope = 3/2.

21. The formula for Slope-Intercept Form is:
‘b’ is the y-intercept.
‘m’ is the slope.
On the next three slides we will graph the three equations:
using their y-intercepts and slopes.

22. 1) Plot the y-intercept as a point on the y-axis
1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.
right 1
up 2
right 1
up 2
2) Plot more points by counting the slope up the numerator (down if negative) and right the denominator. The coefficient, m = 2, so the slope = 2/1.

23. b represents the y-intercept
Important!!!
This is one of the big concepts in Algebra 1. You need to thoroughly understand this!
Slope – Intercept Form
y = mx + b
m represents the slope
b represents the y-intercept

24. Writing Equations
When asked to write an equation, you need to know two things – slope (m) and y-intercept (b).
There are three types of problems you will face.

25. Writing Equations – Type #1
Write an equation in slope-intercept form of the line that has a slope of 2 and a y-intercept of 6.
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
We have both!! Plug them into slope-intercept form
y = mx + b
y = 2x + 6 2 6

26. Writing Equations – Type #2
Write an equation of the line that has a slope of 3 and goes through the point (2,1).
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
We have to find the y-intercept!! Plug in the slope and ordered pair into y = mx + b
1 = 3(2) + b 3
???

27. Writing Equations – Type #2
1 = 3(2) + b
Solve the equation for b
1 = 6 + b
-5 = b
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
y = 3x - 5 3 -5

28. Writing Equations – Type #3
Write an equation of the line that goes through the points (-2, 1) and (4, 2).
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
We need both!! First, we have to find the slope. Plug the points into the slope formula.
Simplify
???
???

29. Writing Equations – Type #3
Write an equation of the line that goes through the points (-2, 1) and (4, 2).
To write an equation, you need two things:
slope (m) =
y – intercept (b) =
It’s now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use?
I’m using (4, 2) because both numbers are positive.
2 = (4) + b
???

30. Writing Equations – Type #3
2 = (4) + b
Solve the equation for b
2 = b
To write an equation, you need two things:
slope (m) =
y – intercept (b) =

31. Thank you so much