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

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

Linear Equations Sara has 4 hours after dinner to study and do x 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.

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.

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:

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

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.

Slope-Intercept Form

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

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

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.

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.

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.

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.

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.

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

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) = y – intercept (b) = We have both!! Plug them into slope-intercept form y = mx + b y = 2x + 6 2 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) = 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 #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) = 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. Simplify ??? ???

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 ???

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) =

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