1. Objective- To write a linear equation given a point
and a slope.
Write a linear equation in standard form given:
slope = y-intercept = -2
m = b = -2
y = mx + b
y = 3x + -2
Not in standard form!
-3x -3x
Ax + By = C
-3x + y = -2
Where A, B and C
are integers. or
3x - y = 2

2. y = mx + b y = x - 2 Not in standard form! Ax + By = C - x - x
Write a linear equation in standard form given: 1
slope = y-intercept = -2 4
y = mx + b 1
y = x - 2
Not in standard form! 4
Ax + By = C 1 1
- x x 4 4
Where A, B and C
are integers. 1
x + y = -2 4 1 4
- x + y = -2
No fractions! 4
- x + 4y = -8
x - 4y = 8 or

3. -1 (x,y) y = mx + b -1 -1 y = x + y = x + b -1 4 = (2) + b -2 4 = + b
Write a linear equation in standard form given: -1
slope = point = (2,4) 5
(x,y)
y = mx + b -1 22 -1
y = x +
y = x + b 5 5 5 5
+ x x 1 -1
4 = (2) + b 5 -2
4 = b 1 22 5
x + y = 5 5 5 5 2
x + 5y = 22 2 22
= b = 5 5

4. -11 -2 = (1) + b -11 -2 = + b -14 -11 -3 (x,y) y = mx + b -3 -3
Write a linear equation in standard form given: -3
slope = point = (1,-2) 7
(x,y)
y = mx + b -3
-11 -3
y = x +
y = x + b 7 7 7
+ x x 3 7 -3
-2 = (1) + b 7 -3
-2 = b
-11 3 7
x + y = 7 7 7 3 7
3x + 7y = -11 3
= b 7
-14
-11 3
= b = 7 7 7

5. -12 - x - x -3 -12 - - -3x + 5y = -12 -12 (x,y) y = mx + b (4,0)
Write a linear equation in standard form given: 3
slope = x-intercept = 4 5
(x,y)
y = mx + b
(4,0)
-12 3
y = x + 3
y = x + b 5 5 5
- x x 3 5 3
0 = (4) + b 5 12 -3
-12
0 = b 5
x + y = 5 5 5 5 12
-3x + 5y = -12
-12
= b or 5
3x - 5y = 12

6. Finding an Equation Given Two Points
y = mx + b 1
Write the equation of
the line which contains:
y = x + b 3 1
5 = (4) + b
(-2, 3) (4, 5) 3
(x, y) 4
y2- y1
5 = b 3
Slope (m) =
x2- x1 4 15 4
b = 5 - - =
5 - 3 3 3 3 2
Slope (m) = =
4 - -2 11 6
b = 3 1 11 1
y = x +
m = 3 3 3

7. -3 = b Write the equation of the line which contains: (0, -3) (4, 8)
(0, -3) (4, 8)
y = mx + b
(x, y) 11
y = x + b
y2- y1 4
Slope (m) =
x2- x1 11
8 = (4) + b 4
8 - -3 11
Slope (m) = =
4 - 0
8 = b 4 11
m =
-3 = b 4
b = -3 11
y = x - 3 4

8. -12 -12 Use the x-y chart below to write a linear
equation that satisfies all the points. x y
y = mx + b +2 +6
y = 3x + b +3 +9
10 = 3(4) + b +2 +6 +5
+15
10 = 12 + b
y2- y1
10 - 4
-2 = b
m = =
x2- x1
4 - 2 6
m = = 3
y = 3x - 2 2

9. The graph below represents the volume of water
in a tank (y) over time (x). Find the equation that
describes y in terms of x. 60 50 40 30 20 10
Water Level (Gal.)
Hours

10. The graph below represents the total cost of a
taxi ride (C) over miles driven (n). Find the
equation that describes C in terms of n. C 60 50 40 30 20 10
Total Cost n
Miles

11. Point-Slope Form Write the equation of a line in point-slope form
that passes through (2,5) with a slope of -3.

12. Forms of the Linear Equation
Standard Form
Slope-Intercept Form
Point-Slope Form

13. Write the equation in slope-intercept form that
passes through (-2,6) with slope of 3.

14. Write the equation in slope-intercept form that
passes through (5,-1) with slope of

15. Write the equation of the line below in slope-intercept form.y -2 +3 x
(-2, 3)