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SEMINAR P . P . T …. Topic- Slope-intercept form and Equation of a line. Submitted to - Sh.Bharat Bhushan Sir. Submitted by- Mayank Devnani. Equation of a LINE. Given the Slope and Y-Intercept. Just plug them into y = mx + b - PowerPoint PPT PresentationTRANSCRIPT
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