Algebra 1: Graphing Linear Equations and Inequalities in 2 Variables
Name: _______________________________________ Topic D5: Finding the Equation of a Line | VERSION A Give the equations of the lines with the given 5.
−6𝑥 − 2𝑦 = 12 𝑦 = y
slopes and y-­‐intercepts. 1.
5
1
𝑚 = − , 𝑏 = −5 2
4
3
2
𝑦 = 1
1
2.
2
3
4
5
x
5
3
𝑚 = , 𝑏 = −4 𝑦 = Find the slopes and y-­‐intercepts for the following equations by writing them in the form 𝑦 = 𝑚𝑥 + 𝑏 then graph the equation. 3.
−4𝑥 + 𝑦 = 2 𝑦 = For the following problems, the slopes and one point on each line is given. Use the point-­‐slope form to find the equations of the lines in slope-­‐intercept form. y
5
4
3
6.
−2, −7 , 𝑚 = 2 𝑦 = 7.
−3, 0 , 𝑚 = − 2
3
𝑦 = 8.
−2, 5 , 𝑚 = −3 𝑦 = 9.
3, −4 , 𝑚 = 0 𝑦 = 2
1
1
2
3
4
5
x
4.
3𝑥 + 6𝑦 = 18 𝑦 = y
5
4
3
2
1
1
2
3
4
5
x
www.varsitylearning.com 1 Algebra 1: Graphing Linear Equations and Inequalities in 2 Variables
Name: _______________________________________ Topic D5: Finding the Equation of a Line | VERSION A Find the equations, in slope-­‐intercept form, of the lines that pass through the following pairs of points. 10. 2, −8 , (1, −5) 15. Slope = y-­‐intercept = Equations: 𝑦 = 𝑦 = y
5
4
3
11. −1, 4 , (−2, 7) 2
𝑦 = 1
1
12. 6, 7 , (2, 1) 2
3
4
5
x
𝑦 = 16. Find the equation of the line with x-­‐intercept 13. 3, −2 , (6, −3) 𝑦 = (2, 0) and y-­‐intercept (0, 1). 𝑦 = Find the slope and y-­‐intercepts in the following graphs. Then write the equations of the lines in slope-­‐intercept form. 17. Find the slope of the line parallel to the line that crosses (2, −2) and the y-­‐intercept is (0, −3). 𝑚 = 14. Slope = y-­‐intercept = 18. Find the slope of the line parallel to the line that Equations: 𝑦 = passes through (3, 2) and (−2, −3). y
𝑚 = 5
4
19. Find the slope of a line perpendicular to the line 3
that passes through (−1, 2) and (2, −3). 2
1
1
2
3
4
5
𝑚 = x
20. Find the slope of a line perpendicular to the line that passes through (2, −3) and (−4, −2). 𝑚 = www.varsitylearning.com 2 Algebra 1: Graphing Linear Equations and Inequalities in 2 Variables
Name: _______________________________________ Topic D5: Finding the Equation of a Line | VERSION A Give the equations of the lines with the given 5.
−6𝑥 − 2𝑦 = 12 𝑦 = −3𝑥 − 6 y
slopes and y-­‐intercepts. 1.
5
1
𝑚 = − , 𝑏 = −5 2
4
3
2
1
𝑦 = − 𝑥 − 5 2
1
1
2.
2
3
4
5
x
5
3
𝑚 = , 𝑏 = −4 5
3
𝑦 = 𝑥 − 4 Find the slopes and y-­‐intercepts for the following equations by writing them in the form 𝑦 = 𝑚𝑥 + 𝑏 then graph the equation. 3.
−4𝑥 + 𝑦 = 2 For the following problems, the slopes and one point on each line is given. Use the point-­‐slope form to find the equations of the lines in slope-­‐intercept form. 𝑦 = 4𝑥 + 2 y
5
4
6.
−2, −7 , 𝑚 = 2 𝑦 = 2𝑥 − 3 7.
−3, 0 , 𝑚 = − 𝑦 = − 𝑥 − 2 8.
−2, 5 , 𝑚 = −3 𝑦 = −3𝑥 − 1 9.
3, −4 , 𝑚 = 0 𝑦 = −4 3
2
1
1
2
3
4
5
x
2
3
2
3
4.
1
2
3𝑥 + 6𝑦 = 18 𝑦 = − 𝑥 + 3 y
5
4
3
2
1
1
2
3
4
5
x
www.varsitylearning.com 3 Algebra 1: Graphing Linear Equations and Inequalities in 2 Variables
Name: _______________________________________ Topic D5: Finding the Equation of a Line | VERSION A Find the equations, in slope-­‐intercept form, of the lines that pass through the following pairs of points. 10. 2, −8 , (1, −5) 1
2
15. Slope = − y-­‐intercept = 0, −5 1
2
𝑦 = −3𝑥 − 2 Equations: 𝑦 = − 𝑥 − 5 y
5
4
11. −1, 4 , (−2, 7) 𝑦 = −3𝑥 + 1 3
2
1
1
2
3
4
5
x
3
2
12. 6, 7 , (2, 1) 𝑦 = 𝑥 − 2 1
3
13. 3, −2 , (6, −3) 16. Find the equation of the line with x-­‐intercept (2, 0) and y-­‐intercept (0, 1). 𝑦 = − 𝑥 − 1 1
2
𝑦 = − 𝑥 + 1 Find the slope and y-­‐intercepts in the following graphs. Then write the equations of the lines in slope-­‐intercept form. 17. Find the slope of the line parallel to the line that crosses (2, −2) and the y-­‐intercept is (0, −3). !
𝑚 = !
14. Slope = −2 y-­‐intercept = 0, 4 18. Find the slope of the line parallel to the line that passes through (3, 2) and (−2, −3). 𝑚 = 1 Equations: 𝑦 = −2𝑥 + 4 y
5
4
19. Find the slope of a line perpendicular to the line that passes through (−1, 2) and (2, −3). 3
2
!
1
1
2
3
4
5
𝑚 = x
!
20. Find the slope of a line perpendicular to the line that passes through (2, −3) and (−4, −2). 𝑚 = 6 www.varsitylearning.com 4