1. Writing Equations
Index Card Activity

2. I. How to Write an Equation of a Line Given m and b
1. Write down y = mx + b
2. Substitute slope for m and y-intercept for b.
3. Simplify the equation

3. Write the equation of the line given m and b.
Ex. 1 Slope is -5 and y-intercept is 2
y = -5x + 2
Ex. 2 Slope is -1/2 and y-intercept is -2
y = -½x – 2

4. II. How to Write an Equation of a Line Given a Graph
Write down y = mx + b
Use any 2 “good” points on the graph to find the slope, m.
Find the y-intercept on the graph, b.
Substitute slope for m and y-int for b into the equation y = mx + b.

5. 5. Write the equation of this graph
m = 6−2 5−0 = 4 5
y = mx + b
y = x + b
y = x + 2 

6. 7. Write the equation of Type equation here.this graph
M = 2 −(−1) 0 −1 = 3 −1 = -3
y = mx + b
y = -3x + b  
y = -3x + 2

7. III. How to Write an Equation of a Line Given m and a point
Write down y = mx + b.
Substitute slope for m and the point (x, y).
Solve for b.
Substitute m and b back into the equation.

8. Write the equation of the line given m and a point
Ex 13: m = 2 Point: (2, 3)
y = mx + b
3 = 2 (2) + b
3 = 4 + b (subtract 4 from both sides)
-1 = b
y = 2x – 1

9. 3 = 10 + b (subtract 10 from both sides) -7 = b y = -2x – 7
Write the equation of the line given m and a point
Ex 15: m = -2 Point: (-5, 3)
y = mx + b
3 = -2 (-5) + b
3 = 10 + b (subtract 10 from both sides)
-7 = b
y = -2x – 7

10. IV. How to Write an Equation of a Line Given TWO points
Write down y = mx + b.
Use the slope formula to find m.
Pick one of the ordered pairs & substitute slope for m and the point (x, y).
Solve for b.
Substitute m and b into the equation.

11. Equation of a Line - Given 2 points
Ex: (2, 3) (4, 5)
y = mx + b
3 = 1(2) + b
3 = 2 + b (subtract 2 both sides)
b = 1
y = x + 1

12. Equation of a Line - Given 2 points
Ex: (2, 2) (0, 4)
y = mx + b
y = -1x + b
4 = -1 (0) + b
4 = 0 + b
4 = b
y = -x + 4

13. How to Write an Equation of a Line PARALLEL to another and given a point
1. Given equation should be solved for y (y = mx + b)
Write down the slope of that line
Substitute m and (x, y) in y = mx + b.
Solve for b.
Write the equation using m and b.

14. Write a line parallel to the line y = 3x – 5 and passes through the point (-5, -2).
y = mx + b
y = 3x + b
-2 = 3 (-5) + b
-2 = b (add 15 to each side)
13 = b
Work on left side of t-chart, step by step notes on right side
y = 3x + 13

15. Write a line parallel to the line 2x + y = 3 and passes through the point (-2, 5). Rewrite equation: y = -2x + 3
y = mx + b
Y = -2x + b
5 = -2 (-2) + b
5 = 4 + b (subtract 4 from each side)
1 = b
Work on left side of t-chart, step by step notes on right side
y = -2x + 1

16. 1. Given equation should be solved for y (y = mx + b)
How to Write an Equation of a Line PERPENDICULAR to another and given a point
1. Given equation should be solved for y (y = mx + b)
Write down the OPPOSITE RECIPROCAL slope of that line
Substitute m and (x, y) in y = mx +b.
Solve for b.
Write the equation using m and b.

17. Write a line perpendicular to the line y = ½ x – 2 and passes through the point (1, 0).
Find opposite reciprocal of ½: -2
y = mx + b
y = -2x + b
0 = -2 (1) + b
0 = -2 + b (add 2 to each side)
2 = b
Work on left side of t-chart, step by step notes on right side
y = -2x + 2

18. Write a line perpendicular to the line 2x + 3y = 9 and passes through the point (6, -1).
Rewrite equation: 3y = -2x (divide both sides by 3)
y = − 2 3 x + 3
Find opposite reciprocal of − 2 3 : 3 2
y = mx + b
y = x + b
-1 = (6) + b
-1 = b
-1 = 9 + b (subtract 9 from both sides)
-10 = b
Work on left side of t-chart, step by step notes on right side
y = 3/2 x – 10