SEMINAR P.P.T.. Topic- Slope-intercept form and Equation of
SEMINAR P.P.T.. Topic- Slope-intercept form and Equation of a line Submitted to - Sh.Bharat Bhushan Sir SUBMITTED BY- MAYANK DEVNANI I L a f o n o i t
a u q E E N 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
A E N I L I T A U Q E R S N
O Linear Equations Vocabulary 1) 2) 3) 4) 5) linear equation linear function standard form y-intercept x-intercept
Linear Equations y 6 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. 4 x y
4 2 x 0 -2 -2 2 0 An equation such as x + y = 4 is called a linear equation.
4 6 Linear Equations A linear function is a function whose ordered pairs satisfy a linear equation. Any linear function can be written in the form are real numbers. f(x) = mx + b, where m and b State whether each function is a linear function. Explain. a) b)
f(x) = 10 5x Yes! g(x) = x4 5 No! It can be written as f(x) m = 5, b = 10 x c) h(x, y) = 2xy
= 5x + 10 has an exponent other than 1. 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
Write the equation in Standard Form: y 3x 4 3x y 4 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 The y-coordinate of the point at which the graph y - intercept crosses the y-axis is called the ____________.
(0, 3) (-4, 0) x The x-coordinate of the point at which the graph x - intercept crosses the x-axis is called the ____________. Linear Equations Find the x-intercept and the y-intercept of the graph of the equation. Then graph the equation. 5 x 3 y 15 The x-intercept is the value of x when y = 0. 5 x 3(0) 15
y (0, 5) 5 x 15 x 3 The y-intercept is the value of y when x = 0. 5(0) 3 y 15 3 y 15 y 5 x (3, 0)
t p e c r e t n I m e r p o o l
F S FORMULA FOR FINDING SLOPE The formula is used when you know two points of a line. They look like A( X 1 , Y1 ) and B ( X 2 , Y2 ) RISE X 2 X 1 X 1 X 2 SLOPE RUN Y2 Y1 Y1 Y2
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 X 1 Y1 X2 Y2 X 2 X1 (10) ( 4) Y2 Y1 SUBSTITUTE INTO FORMULA ( 4) (8) (10) ( 4)
10 4 14 7 Then Simplify ( 4) (8) 4 ( 8) 12 6 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. These equations are all in SlopeIntercept Form: y 2x 1 y x 4 3 y x 2 2 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 Constant = 1, y-intercept = 1. y x 4 Constant = -4, y-intercept = -4. 3 y x 2 2
Coefficient = 2, slope = 2. 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: 3
y 2x 1, y x 4, y x 2 2 using their y-intercepts and slopes. y 2x 1 right 1 right 1 1) Plot the y-intercept as a point on the y-axis. The constant, b = 1, so the y-intercept = 1. up 2 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. 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 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 #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) = 2 y intercept (b) = 6 We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6
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) = 3 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 Writing Equations Type #2 1 = 3(2) + b Solve the equation for b
1=6+b -6 -6 -5 = b To write an equation, you need two things: slope (m) = 3 y intercept (b) = -5 y = 3x - 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. Simplify 2 1 m 4 ( 2) 1 m 6 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:
1 slope (m) = 6 y intercept (b) = ??? Its now a Type #2 problem. Pick one of the ordered pairs to plug into the equation. Which one looks easiest to use? Im using (4, 2) because both numbers are positive. 2 = 1 (4) + b 6 Writing Equations Type #3 1 2 = (4) + b 6
Solve the equation for b 2= 2 +b 3 2 2 3 3 1 1 b 3 To write an equation, you need two things: 1 slope (m) =
SWMM being applied to part of Exeter. Red shows the areas modeled in detail. ... a patient's illness has progressed and it requires direct medical attention. For example, the patient may need surgery to address an injury or illness. ......
raportareafără riscul sancţiunilorși de norme clare privind . confidenţialitatea. Tipuriledeincidentecarepot fi raportate variază. Cu toate acestea,o . definiţielargă permite raportarea oricăror preocupări, inclusiv incidente . evitate la limită și incidente care nu au cauzat niciun prejudiciu, oferind o
Seditious libel is another example of a vague term that has no specific definition in the Constitution. Generally speaking, it refers to defaming or ridiculing officers of the government, the Constitution, laws, or government policies that might jeopardize "public peace"...
The real exchange rate adjusts to equate demand (net exports) with supply (NCO) in the foreign exchange market. Students are much less likely to answer exam questions incorrectly if they carefully study this order and direction of causality among the...
The Spread of Absolutism. Out of the Thirty Years' War, Prussia and emerged in the 17th and 18th century as two great absolute European Powers. At the beginning of the 17th century, Spain was the most populous empire in the...
What are five characteristics of professionalism? PROFESSIONAL Discuss professionalism for each of the areas listed below: Appropriate clothes and grooming Appropriate language Respect titles and salutations Use of technology: phone/cell phones, email, pagers, internet, etc. PROJECT Complete the project titled,...
Ready to download the document? Go ahead and hit continue!