2.03 Writing Linear Equations

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Practice Problem #1

Write an equation of a line in slope intercept form from the table of values.

x	y
-4	-18
4	6
6	12
10	24
12	30

Start by finding the slope. Use points (4,6) and (6, 12).

m = 3

Ok, now you have slope = 3. Plug one of the points into the equation to find b. Let’s use (4, 6).

y = mx + b
6 = (3)(4) + b
6 = 12 + b Use order of operations to simplify.
-6 = b Isolate the b values.
Now that you know m and b, plug those values into the slope intercept form to find the equation of the line.
y = 3x - b

Practice Problem #2

Write an equation of a line in slope intercept form using the graph.

Starting by finding the slope. Use the x-intercept and y-intercept to calculate the slope because those values will be easy to calculate. You could use any two points on the line to calculate slope, these are just convenient for calculations.

OK, now that we have m, we need to find b. What is b on this graph?

b(0, 2)

Now that we know m and b, we can substitute them into slope intercept form to find the equation for this line.

y = mx + b

Practice Problem #3

Write an equation of a line in slope intercept form from the table of values.

x	y
6	8
10	16
12	20
15	26
20	36

Start by finding the slope. Use points (6,8) and (10, 16).

m = 2

Now that we know that slope (m) = 2, we can substitute that value of x and y into slope intercept form to find the intercept. Let’s use the point (6, 8).

y = mx + b
8 = (2)(6)+ b
8 = 12 + b Use order of operations to simplify.
-4 = b Isolate the b values.
Now that you know m and b, plug those values into the slope intercept form to find the equation of the line.
y = 2x - 4

Practice Problem #4

Rewrite the linear equation from standard form to slope intercept form.
3x + 4y = 12

To rewrite this equation, for first need to isolate the y-term on the left side. What should you subtract to do this?

3 - 3x + 4y = -3x + 12
4y = –3x + 12

Multiple Choice Problems

1. Find the equation using the point-slope formula:
   (-4, 8) m = -6
   1. y = -5x - 37
   2. y = -4x - 27
   3. y = -6x - 16
   4. y = -5x - 59

   Answer: c. y = -6x - 16
   y - 8 = -6(x - -4)
   y - 8 = -6x - 24
   y = -6x - 16

2. Find the equation using the point-slope formula:
   (4, 3) m = -3
   1. y = -4x + 25
   2. y = -3x - 83
   3. y = -3x + 15
   4. y = -3x - 96

   Answer: c. y = -3x + 15
   y - 3 = -3(x - -4)
   y - 3 = -3x + 12
   y = -3x + 15

3. Find the equation using the point-slope formula:
   (3, 4) m = 4
   1. y = 4x - 8
   2. y = 8x - 6
   3. y = 8x - 4
   4. y = 6x - 3

   Answer: a. y = 4x - 8
   y - 4 = 4(x - 3)
   y - 4 = 4x - 12
   y = 4x - 8

4. Find the equation using the point-slope formula:
   (-3, 7) m = -5
   1. y = -3x - 8
   2. y = -9x - 7
   3. y = -5x - 8
   4. y = -5x - 7

   Answer: c. y = -5x - 8
   y - 7 = -5(x - -3)
   y - 7 = -5x - 15
   y = -5x - 8

5. Find the equation using the point-slope formula:
   (2, -3) m = 2
   1. y = 7x - 2
   2. y = 7x - 3
   3. y = 5x - 9
   4. y = 2x - 7

   Answer: d. y = 2x - 7
   y - -3 = 2(x - 2)
   y + 3 = 2x - 4
   y = 2x - 7

6. Find the equation using the point-slope formula:
   (-5, 2) m = -2
   1. y = -2x - 8
   2. y = -8x - 3
   3. y = -2x - 4
   4. y = -4x - 4

   Answer: a. y = -2x - 8
   y - 2 = -2(x - -5)
   y - 2 = -2x - 10
   y = -2x - 8