SEMINAR P.P.T…..

Submitted to - Sh.Bharat Bhushan Sir

SUBMITTED BY- MAYANK DEVNANI

Topic- Slope-intercept form and Equation of a line

Equation of a

LINE

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

Given a Graph• Find the slope and y-intercept.• Then, plug into y = mx + b

• Example:• Write an equation of the line shown.

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

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

LINEAR EQUATIONS

Linear Equations

1) linear equation2) linear function3) standard form4) y-intercept5) x-intercept

y

x

6

0

4-2-2

2

6

-2 6

0

-2

6

2

4

4 yx

Sara has 4 hours after dinner to study and dohomework. She has brought home algebra 2and chemistry.

If she spends x hours on algebra and y hours on chemistry, a portion of the graphof 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.

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 bare 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 + 10m = – 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.

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

Linear Equations

Write the equation in Standard Form:

43 xy

43 yx

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 connectthem with a line.

y

x

The y-coordinate of the point at which the graphcrosses the y-axis is called the ____________.y - intercept

The x-coordinate of the point at which the graphcrosses the x-axis is called the ____________.x - intercept

(0, 3)

(-4, 0)

Linear Equations

Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.

y

x

The x-intercept is the value of x when y = 0.(0, 5)

(3, 0)

Linear Equations

1535 yx

15)0(35 x

155 x

3x

The y-intercept is the value of y when x = 0.

153)0(5 y

153 y

5y

Slope-Interce

pt

Form

FORMULA FOR FINDING SLOPE

21

21

12

12

YY

XX

YY

XX

RUN

RISESLOPE

The formula is used when you know two points of a line.

),(),( 2211 YXBandYXAlikelookThey

Find the slope of the line between the two points (-4, 8) and (10, -4)

If it helps label the points.1X 1Y

2X 2Y

Then use the formula

12

12

YY

XX

)8()4(

)4()10(

FORMULAINTOSUBSTITUTE

6

7

12

14

)8(4

410

)8()4(

)4()10(

SimplifyThen

Graphing Linear Equations

In Slope-Intercept Form

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.

y 2x 1

y x 4

y 32

x 2

These equations are all in Slope-Intercept Form:

Notice that these equations are all solved for y.

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.

y 2x 1

y x 4

y 3

2x 2

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.

The formula for Slope-Intercept Form is:

y mx b;• ‘b’ is the y-intercept.

• ‘m’ is the slope.

On the next three slides we will graph the three equations:

y 2x 1, y x 4, y 3

2x 2

using their y-intercepts and slopes.

y 2x 1

1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1.

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.

up 2

right 1 up 2

right 1

Important!!!

This is one of the big concepts in Algebra 1. You need to thoroughly

understand this!Slope – Intercept Form

y = mx + bm represents the slope

b represents the y-intercept

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.

Writing Equations – Type #1Write 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 + by = 2x + 6

26

Writing Equations – Type #2Write 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???

Writing Equations – Type #21 = 3(2) + b

Solve the equation for b 1 = 6 + b -6 -6

-5 = bTo write an equation, you need two things:

slope (m) =y – intercept (b) =

y = 3x - 5

3-5

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.

Simplify2 1

4 ( 2)m

??????

1

6m

Writing Equations – Type #3Write 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

1

6???

1

6

Writing Equations – Type #32 = (4) + b

Solve the equation for b 2 = + b

To write an equation, you need two things:slope (m) =y – intercept (b) =

1

62

32

3

11

3b

2

3

1

6 11

3

1 11

6 3y x

Thank you so much