Algebra 1 Unit 4 Quiz Study Material PDF

Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________...

Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples To write the equation of the line passing through point (x1, y1) with slope (m), you can use the point-slope formula: WRITING LINEAR Point-Slope Formula: EQUATIONS Point -Slope Formula: (Given a Point and Slope) *Be sure to distribute and solve for y!* Directions: Write the equation of the line that passes through the given point and has the given slope. Write all final answers in slope-intercept EXAMPLES form. 1. (4, 1); slope = 2 2. (2, 4); slope = 1 2 2 3 3. (-6, 0); slope = 4. (-8, -1); slope = − 3 4 5. (4, -3); slope = -1 6. (0, -9); slope = 4 © Gina Wilson (All Things Algebra®, LLC), 2012-2017  1 8. (3, -8); slope = -3 7. (-12, -5); slope = 3 2 10. (-4, -7); slope = 1 9. (5, -9); slope = − 5 4 12. (4, 9); slope = 5 11. (-6, -1); slope = − 3 13. (3, -4); slope = 0 5 14. (-6, -8); slope = 6 1 16. (7, -8); slope = -2 15. (-4, 1); slope = − 4 © Gina Wilson (All Things Algebra®, LLC), 2012-2017 Name: ___________________________________ Unit 4: Linear Equations Date: ________________________ Bell: ______ Homework 6: Writing Linear Equations (Given Point & Slope) Directions: Given the point and slope, write the equation of the line. 1. (4, 2); slope = 3 2. (0, 3); slope = -2 3. (1, -7); slope = -1 3 4. (-5, -3); slope =  5 1 2 5. (-8, 6); slope = 6. (9, -4); slope =  4 3 5 3 7. (6, -6); slope = 8. (-8, 9); slope =  6 2 1 9. (-2, -11); slope = 4 10. (-4, 0); slope = 2 © Gina Wilson (All Things Algebra®, LLC), 2012-2017 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples To write a linear equation that passes through two points, (x1, y1) and (x2, y2), use the slope formula followed by WRITING LINEAR the point-slope formula: EQUATIONS Slope Formula Point-Slope Formula (Given Two Points) Directions: Write the equation of the line that passes through the given two points. Write all final answers in slope-intercept form. EXAMPLES 1. (-3, 7) and (1, -1) 2. (-6, -7) and (3, -4) 3. (2, -1) and (4, -6) 4. (1, 6) and (2, 5) 5. (-8, 1) and (0, -5) 6. (-3, -8) and (2, 7) © Gina Wilson (All Things Algebra®, LLC), 2012-2017 7. (-9, -14) and (3, 2) 8. (-6, -3) and (-4, -1) 9. (-4, 7) and (6, 2) 10. (1, 1) and (-1, -9) 11. (4, -1) and (0, 2) 12. (-2, -2) and (1, -5) 13. (3, -5) and (2, -1) 14. (-3, 14) and (2, -1) © Gina Wilson (All Things Algebra®, LLC), 2012-2017 Name: ___________________________________ Unit 4: Linear Equations Date: ________________________ Bell: ______ Homework 7: Writing Linear Equations (Given Two Points) Directions: Write a linear equation that passes through the given two points. 1. (-4, -2) and (4, 0) 2. (3, 4) and (0, 5) 3. (0, 1) and (5, 3) 4. (2, -2) and (0, -1) 5. (0, 5) and (-5, 1) 6. (1, 3) and (-3, -5) 7. (1, 4) and (6, -1) 8. (3, 3) and (1, -3) 9. (-12, 14) and (6, -1) 10. (-1, 4) and (0, -1) © Gina Wilson (All Things Algebra®, LLC), 2012-2017  Partner A: _________________________ Partner B: _________________________ WHY WAS THE CAT KICKED OUT OF SCHOOL? Given either a point and a slope, or two points, write each equation in slope-intercept form. Partner A should do the left side and Partner B should do the right side. One will have a letter and the other a number. Write the letter in the matching numbered box at the bottom of the page. SET 1 2 8. (2, -2); slope = 1 _______________________ E. (-3, 0); slope = ______________________ 3 3 H. (6, 2) and (-3, -7) ______________________ 3. (4, 1); slope = _______________________ 2 S. (-4, -6) and (3, 8) ______________________ 10. (3, 4) and (-6, -2) ______________________ W. (-2, -8) and (6, 4) ______________________ 5. (-3, -4); slope = 2 _______________________ SET 2 4 1 A. (-9, 17); slope = − ______________________ 12. (-4, -5); slope = _______________________ 3 2 C. (-3, 9) and (0, 1) _______________________ 6. (3, 1) and (9, -7) _______________________ E. (1, -8); slope = -1 _______________________ 7. (3, -7); slope = − 8 _______________________ 3 A. (2, -2) and (8, 1) _______________________ 2. (5, -12) and (-3, -4) ______________________ SET 3 H. (-12, 4) and (0, 2) ______________________ 9. (-6, -4) and (12, 11) _______________________ 5 7 E. (6, 6); slope = _______________________ 4. (2, -8); slope = − _______________________ 6 2 H. (-8, -4) and (4, -7) _______________________ 11. (5, 1) and (10, 5) _______________________ 4 1 T. (-5, -7); slope = _______________________ 13. (6, 1); slope = − _______________________ 5 6 A. (-4, 13) and (-2, 6) _______________________ 1. (-4, -5); slope = − 1 _______________________ 4 1 2 3 4 5 6 7 8 9 10 11 12 13 ! © Gina Wilson (All Things Algebra®, LLC), 2012-2017  I can write Linear Equations in SLOPE-INTERCEPT FORM GIVEN: The Slope and y-Intercept 1 slope = ; y-intercept = -5 3 1 2 1 A Graph 1 An Equation in Standard Form 4x – 2y = 14 A Point and Slope (-1, 3); slope = -3 Two Points (-4, -7) and (8, -13) © Gina W ilson (All Things Algebra ®, LLC), 2012-2017 Name: ___________________________________ Unit 4: Linear Equations Date: ________________________ Bell: ______ Homework 8: Writing Linear Equations REVIEW Directions: Write the linear equation in slope-intercept form given the following: 2 1. slope = ; y-intercept = 0 2. slope = 1; y-intercept = -4 7 3.1 1 4. 611 1 1 1 1 1 5. 2x + 5y = 35 6. 2x – y = 4 7. x – 6y = -30 8. 5x – 4y = -12 5 9. (-2, -3); slope = 10. (2, -4); slope = -3 2 11. (0, 2) and (4, -4) 12. (-2, -4) and (-3, -3) © Gina W ilson (All Things Algebra ®, LLC), 2012-2017 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples Parallel Definition: ________________________________________________________________ Lines Algebraically, how do we know if two lines are parallel? Perpendicular Definition: ________________________________________________________________ Lines Algebraically, how do we know if two lines are perpendicular? What are Some examples: Negative 3 7 Reciprocals? 1) & 2) 2 & 3) − & 4) 1 & 5) 0 & 4 8 Determine if segments AB and CD are parallel, perpendicular, or neither: Given 1. AB formed by (-2, 3) and (2, 6) 2. AB formed by (0, 2) and (5, 4) CD formed by (-1, 0) and (3, 3) CD formed by (1, 8) and (3, 3) Ordered Pairs 3. AB formed by (-1, 8) and (2, 6) 4. AB formed by (2, 3) and (-1, 4) CD formed by (-1, 2) and (3, 3) CD formed by (-5, 3) and (-4, 6) © Gina Wilson (All Things Algebra®, LLC), 2012-2017  5. AB formed by (0, -2) and (0, 7) 6. AB formed by (-4, 7) and (-2, 6) CD formed by (3, -5) and (6, -5) CD formed by (2, -2) and (-8, 3) 7. AB formed by (3, 1) and (3, -4) 8. AB formed by (-3, 8) and (3, 2) CD formed by (-4, 1) and (-4, 5) CD formed by (7, 1) and (5, -1) 9. y = 7x + 2 and y = 7x – 1 4 5 10. y = x − 8 and y = − x + 3 5 4 Given Equations 1 1 12. x + 6y = 30 and 3y = 18x – 6 11. y = − x + 2 and y = x 3 3 1 14. 3x – y = 2 and 12x – 4y = 4 13. 5x – y = 4 and y = − x+7 5 15. y = x + 3 and y = -x – 5 16. y = 6 and x = -1 © Gina Wilson (All Things Algebra®, LLC), 2012-2017 PARALLEL, PERPENDICULAR, OR NEITHER? Directions: Determine whether the lines given in each box are parallel, perpendicular, or neither. Color the boxes as follows: Parallel Lines: Yellow Perpendicular Lines: Light Blue Neither: Uncolored 2 1 y= − x+3 y= − x y = 3x – 7 5 4 y = 3x + 1 2 y= x+8 y = 4x – 5 5 2x + 7y = 28 y = -5x + 1 3x + 2 y = 8 7 x – 2y = 4 x – 5y = 30 2x + 3y = -12 1 y = -4x – 1 x+y=7 y= x+9 3 8x + 2y = 14 x–y=9 x – 3y = 3 -9x + 12y = 24 4x + 9y = 18 5x – 10y = 20 3 y = 4x + 9 y = -2x + 6 y= x–5 4 5 y=x–3 10x + 8y = 16 y= x+7 3 x–y=8 5y = 4x – 15 6x – 10y = 10 x – 2y = 18 x=4 x=1 2x + y = 6 x = -6 y = -8 © Gina Wilson (All Things Algebra®, LLC), 2012-2017 Name: ___________________________________ Unit 4: Linear Equations Date: ________________________ Bell: ______ Homework 9: Parallel & Perpendicular Lines (Day 1) Directions: Determine if segments AB and CD are parallel, perpendicular, or neither. 1. AB formed by (-2, 13) and (0, 3) 2. AB formed by (3, 7) and (-6, 1) CD formed by (-5, 0) and (10, 3) CD formed by (-6, -5) and (0, -1) 3. AB formed by (-6, 2) and (-2, 4) 4. AB formed by (-3, 8) and (2, 3) CD formed by (-1, 11) and (5, -7) CD formed by (-4, 6) and (-8, 2) 5. AB formed by (-8, -1) and (-4, 2) 6. AB formed by (6, 5) and (3, -1) CD formed by (0, -3) and (12, 6) CD formed by (2, -5) and (-4, 7) Directions: Determine if the given equations are parallel, perpendicular, or neither. 3 8. 3y = 4x + 15 and 9x + 12y = 12 7. 3x + 2y = 6 and y = − x + 5 2 9. 8x – 2y = 4 and x + 4y = -12 10. 3x + 2y = 10 and 2x + 3y = -3 11. -4y = -2x + 8 and 3x – 6y = 6 12. y = 8 and x = -1 © Gina Wilson (All Things Algebra®, LLC), 2012-2017 Name: Date: ___________________________________________________ _________________________________ Topic: Class: ___________________________________________________ _________________________________ Main Ideas/Questions Notes/Examples What are we doing? Given a linear equation and a certain point, you can create ANOTHER equation that passes through this point and is WRITING either parallel or perpendicular to the given line. Parallel & Perpendicular Keep in mind the following points: EQUATIONS
Parallel lines have ______________________ slopes.
Perpendicular lines have ___________________ ___________________ slopes. 1. Write the equation of the line that passes through the point (-2, 7) and is PARALLEL to the line y = -4x + 1. PARALLEL EXAMPLES 2. Write the equation of the line that passes through the point (3, -1) and is PARALLEL to the line x – 3y = 9. 3. Write the equation of the line that passes through the point (4, 3) and is PERPENDICULAR to the line y = 2x – 4. PERPENDICULAR EXAMPLES 4. Write the equation of the line that passes through the point (-5, 1) and is PERPENDICULAR to the line 5x + 3y = -21. © Gina Wilson (All Things Algebra®, LLC), 2012-2017  Directions: Write an equation passing through the point that is PARALLEL to the given equation. MORE 5. (-4, -1); y = 2x + 4 1 6. (8, 3); y = − x + 7 PRACTICE 4 7. (4, 5); x – 2y = 14 8. (-6, 7); 5x + 2y = 10 Directions: Write an equation passing through the point that is PERPENDICULAR to the given equation. 3 10. (-3, -2); y = x – 2 9. (3, -3); y = x + 5 4 11. (2, 3); 2x + 10y = 20 12. (-1, -6); x + 3y = 6 © Gina Wilson (All Things Algebra®, LLC), 2012-2017 Name: ___________________________________ Unit 4: Linear Equations Date: ________________________ Bell: ______ Homework 10: Parallel & Perpendicular Lines (Day 2) Directions: Write an equation passing through the point and PARALLEL to the given line. 1. (4, 7); y = 3x + 6 2. (-2, 3); y = -x + 4 1 4. (-8, 2); 5x – 4y = 4 3. (-4, -5); y = x−6 2 5. (-10, 1); 2x + 5y = 15 6. (-5, -1); 2y = 2x – 4 Directions: Write an equation passing through the point and PERPENDICULAR to the given line. 1 8. (4, -1); y = 2x – 4 7. (-2, -2); y = − x + 9 5 3 10. (2, -5); x – 4y = 20 9. (-3, 5); y = x−4 4 11. (10, 7); 5x – 6y = 18 12. (-2, 2); 6x + 3y = -9 © Gina Wilson (All Things Algebra®, LLC), 2012-2017