3-3 Slope-Intercept Form

A.2B Write linear equations in two variables in various forms, including y=mx + b, Ax + By=C, and y-y =m(x-x ), given one point and the slope ₁ ₁and given two points.

• Hudson is already 40 miles away from home on his drive back tocollege. He is driving 65 mi/h. Write an equation that models thetotal distance d travelled after h hours. What is the graph of theequation?

• When Phil started his new job, he owed the company $65 for hisuniforms. He is earning $13 per hour. The cost of his uniforms iswithheld from his earnings. Write an equation that models the totalmoney he has m after h hours of work. What is the graph of theequation?

Write an equation in slope-intercept form of the line that passes through the

given points.19. (3, 5) and (0, 4)

20. (2, 6) and (–4, –2)

21. (–1, 3) and (–3, 1)

22. (–7, 5) and (3, 0)

23. (10, 2) and (–2, –2)

24. (0, –1) and (5, 6)

25. (3, 2) and (–1, 6)

26. (–4, –3) and (3, 4)

27. (2, 8) and (–3, 6)

Find the slope and the y-intercept of the graph of each equation.

36. y + 4 = –6x 37. x = –4 38. 3y – 12x + 6 = 0

39. (x – 9) 40. x = 0x 41. 2y + 6a – 4x = 01– 5 =3

y2–5

y

Point-Slope Form

• You can use the slope of a line and any point on the line to write and graph an equation of the line. Any two equations for the same line are equivalent.

• Point Slope form of an equation of a nonvertical line with slope m and through point (x - y ) is y - y = m(x - x )₁ ₁ ₁ ₁

Writing an Equation in Point Slope Form

• A line passes through (-3,6) and has slope -5. What is an equation of the line?• y - y = m(x - x )₁ ₁ use point-slope form• Y – 6 = -5[x – (-3)] substitute (-3, 6) for (x - y ) ₁ ₁and -5 for m• y – 6 = -(x + 3) simplify inside grouping symbols

Using Two points to write an Equation p121

• (1, 3); m = 5

• (–2, –1); m = –3• (4, –7); m =

•(5, 1), (0, 2)• (–3, –2), (2, 3)

• (–2, –3), (4, 3)

Write an equation in point-slope form of each line.

Standard Form

•One form of a linear equation, called Standard Form, allows you to find intercepts quickly. You can use the intercepts to draw the graph.

Standard form of a linear Equation

• The standard form of a linear equation is Ax + By = C , where A, B, and C are real numbers, and A and B are not both zero.

Find x and y intercepts and Slope

• What are the x and y intercepts and slope of the graph of 3x + 4y = 24?

• Re-Write the equation in slope-intercept form.

Graphing a line Using Intercepts

• What is the graph of x – 2y = -2?• Know: An equation of the line

• Need: the coordinates of at least two points on the line

• Find and plot the x and y intercepts. Draw a line through the points.

Find the x- and y-intercepts and the slope of the graph of each equation.

• 1. x + y = 7

• 2. x – 3y = 9

• 3. 2x + 3y = –6

• 4. –4x – 2y = –8

Writing Linear Equations in Standard form

• What is an equation, in standard form, of the line through (-5,7) with slope ?

Writing Linear Equations in Standard form

• (4, –2), (5, –4)

• (1, 1), (–5, 7)

• (–3, 2), (–4, 10)

Using Standard Form as a Model

• An online store sells songs for $1 each and movies for $12 each. You have $60 to spend.• Write and graph the linear equation that describes the items you

can purchase if you spend the full $60. What are three combinations of numbers of songs and movies you can purchase?

Using Standard Form as a Model

• You have only nickels and dimes in your piggy bank. When you run the coins through a change counter, it indicates you have 595 cents. Write and graph an equation that represents this situation. What are three combinations of nickels and dimes you could have? What are reasonable domain and range values for your function in terms of this real-world situation? What is the zero of the function and what does it mean in this situation?

For each graph, find the slope and x- and y-intercepts. Then write an equation in standard form using

integers.

Write an equation for each horizontal or vertical line.

Using the graph write the equation of the line using all three forms.