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

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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)

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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) =

1 6 1 y y intercept (b) = 1 6 3 1 x 1 3 n a h T

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