1.Use the given points to find the following: (− 7, 5) and (14, − 1) (− 1) − 7 5 – – 14 1 −7−7 5 + – Simplify − 21 6 Reduce m = y 2 – y 1 x 2 – x 1 Formula m = m = m = m = − Substitute © by S-Squared, Inc. All Rights Reserved. a)Find the slope of the line that goes through the two points.

1.Use the given points to find the following: (− 7, 5) and (14, − 1) Slope intercept form: y = mx + b Note: Substitute into the slope intercept form of a line and solve for b. (− 1) = − (14) + b 2 7 Substitute Simplify − 1 = − 4 + b Add = b y-intercept: b = 3 b)Find the y-intercept of the line that goes through the two points.

2 7 1.Use the given points to find the following: (− 7, 5) and (14, − 1) Slope Equation of line y = − x d)Find the slope of a line that is parallel to the line found in part (c). y-intercept − Note: Parallel lines have the same slope. 2 7 m = − b = 3 c)Write the equation of the line in slope-intercept form.

1.Use the given points to find the following: (− 7, 5) and (14, − 1) y = − x Note: Perpendicular lines have slopes that are opposite reciprocals. 7 2 e)Find the slope of the line perpendicular to the line in part (c).

( 1.Use the given points to find the following: (− 7, 5) and (14, − 1) y = x x − 2 7 Standard Form: Ax + By = C where A, B, and C are integers. Multiply each term by the LCD 7 7 ( ( 7 ( 7y = − 2x x + 7y = 21 Add f)Write the equation of the line from part (c) in standard form.

Solve the following system of equations using the graphing method: y = x – 5 x + 2y = − 4 Find the x and y intercepts. y – int.: (0, − 2) x – int.: (− 4, 0) Notice, the y-int. is (0, − 5) and the slope = 1 y = x – 5 Find the y intercept and slope. Answer: (2, − 3) x + 2y = − 4

3a)Graph the following system of linear inequalities: − 12x + 4y > − 12 y ≤ − 2x Find the x and y intercepts. y – int.: (0, − 3) x – int.: ( 1, 0) Notice, the y-int. is (0, 3) and the slope = − 2 y ≤ − 2x + 3 Find the y intercept and slope. − 12x + 4y > − 12

a)Graph the following system of linear inequalities: − 12x + 4y > − 12 y ≤ − 2x + 3 Use (0, 0) as a test point. y ≤ − 2x + 3 − 12x + 4y > − 12 − 12(0) + 4(0) > − 12 0 > − 12 True (0) ≤ − 2(0) ≤ 3 True * Shade region that contains the point (0, 0). Need to shade appropriate region.

3b)Determine if (2, − 1) is a solution to the system of inequalities. − 12x + 4y > − 12 y ≤ − 2x Substitute (2, − 1) into inequalities. y ≤ − 2x + 3 − 12x + 4y > − 12 − 12(2) + 4(− 1) > − 12 False (− 1) ≤ − 2(2) + 3 − 1 ≤ − 1 True * Since the point does not work for both inequalities, it is not a solution. − 28 > − 12 Not a solution

4.Solve the following system of equations using the substitution method: 2x + y = − 5 x + 4y = 1 y = − 2x – 5 Substitute x + 4(− 2x – 5) = 1 x – 8x – 20 = 1 − 7x – 20 = 1 − 7x = 21 x = − 3 Find y 2x + y = − 5 Solve for y Distribute Combine Substitute 2(− 3) + y = − 5 Multiply − 6 + y = − 5 y = 1 Final Answer: (− 3, 1) Solve

5.Solve the following system of equations using the linear combination method: 3x – 2y = 5 x + 4y = − 3 2(3x – 2y = 5) 6x – 4y = 10 x + 4y = − 3 7x = 7 x = 1 Multiply Other Equation Add Equations Find y x + 4y = − 3 Substitute 1 + 4y = − 3 4y = − 4 y = − 1 Final Answer: (1, − 1) Solve

6.Choose any method to solve the system of linear equations. 5x + y = − 8 15x + 3y = − 24 y = − 5x – 8 Substitute 15x + 3(− 5x – 8) = − 24 15x – 15x – 24 = − 24 0x – 24 = − 24 − 24 = − 24 Solve for y Distribute Combine Final Answer: Infinite points of intersection Substitution Method Since what is left is a true statement, we know the lines are the same.

Seven times the first number is five more than the second. Write two Equations: 7x = y + 5 Subtract y: 7.The sum of two numbers is 19. x + y = 19 Assign Variables: Let, x = the first # y = the second # 7x – y = 5 x + y = 19 8x = 24 x = 3 x + y = y = 19 y = 16 Substitute to find y: The first number is 3. The second number is 16. – y The sum of two numbers is 19. Seven times the first number is five more than the second. Combination Method What are the two numbers?

There are 18 coins in all. 8.A collection of dimes and quarters is worth $2.85. A collection of dimes and quarters is worth $2.85. There are 18 coins in all. ( )100 Write two Equations:.10d +.25q = 2.85 Multiply by 100: d + q = 18 Assign Variables: Let, d = the # of dimes q = the # of quarters 10d + 25q = 285 d + q = 18 Multiply by − 10: − 10d + (− 10q) = − d + 25q = q = 105 q = 7 d + q = 18 d + 7 = 18 d = 11 Substitute to find d: There are 7 quarters and 11 dimes. Work hard for you Combination Method How many of each type of coin are there?