EQUATION OF A LINE IN GENERAL FORM WORKSHEET

Problems 1-4 : Write the given equations of lines in general form :

Problem 1 :

y = -2x + 3

Problem 2 :

y = 3x - 1

Problem 3 :

y = 2x/3 - 1

Problem 4 :

y = 5x/4 - 7/6

Problems 5-6 : Write the equations of the given lines in general form :

Problem 5 :

Problem 6 :

Problem 7 :

Write the equation of a line in general form that passes through the point (4, -1) and has slope -2.

Answers

1. Answer :

y = -2x + 3

Add 2x to both sides.

2x + y = 3

Subtract 3 from both sides.

2x + y - 3 = 0

2. Answer :

y = 3x - 1

Subtract 3x from both sides.

-3x + y = -1

Add 1 to both sides.

-3x + y + 1 = 0

Multiply both sides of the equation by -1.

3x - y - 1 = 0

3. Answer :

y = 2x/3 - 1

Multiply both sides of the equation 3.

3(y) = 3(2x/3 - 1)

3y = 3(2x/3) + 3(-1)

3y = 2x - 3

Subtract 2x from both sides.

-2x + 3y = -3

Add 3 to both sides.

-2x + 3y + 3 = 0

Multiply both sides of the equation by -1.

2x - 3y - 3 = 0

4. Answer :

y = 5x/4 - 7/6

In the equation above, we find two different denominators 4 and 6.

The least common multiple of (4, 6) = 12.

Multiply both sides of the equation by 12 to get rid of the denominators 4 and 6.

12(y) = 12(5x/4 - 7/6)

12y = 12(5x/4) + 12(-7/6)

12y = 3(5x) + 2(-7)

12y = 15x - 14

Subtract 15x from both sides.

-15x + 12y = -14

Add 14 to both sides.

-15x + 12y + 14 = 0

Multiply both sides of the equation by -1.

15x - 12y - 14 = 0

5. Answer :

Formula to find the slope of a line when two points are given :

Substitute (x₁, y₁) = (-4, -4) and (x₂, y₂) = (5, 2).

Equation of the line in slope-intercept form :

y = mx + b

Substitute m = 2/3.

y = 2x/3 + b ----(1)

Substitute one of the two points on the line into the above equation to solve for b.

Substitute (5, 2) into the above equation.

2 = 2(5)/3 + b

2 = 10/3 + b

Subtract 10/3 from both sides.

2 - 10/3 = b

-4/3 = b

Substitute b = -4/3 in (1).

y = 2x/3 - 4/3

Multiply both sides by 3 to get rid of the denominators.

3(y) = 3(2x/3 - 4/3)

3y = 3(2x/3) + 3(-4/3)

3y = 2x - 4

Subtract 2x from both sides.

-2x + 3y = -4

Add 4 to both sides.

-2x + 3y + 4 = 0

Multiply both sides of the equation by -1.

2x - 3y - 4 = 0

6. Answer :

Formula to find the slope of a line when two points are given :

Substitute (x₁, y₁) = (-4, 2) and (x₂, y₂) = (4, -4).

Equation of the line in slope-intercept form :

y = mx + b

Substitute m = -3/4.

y = -3x/4 + b ----(1)

Substitute one of the two points on the line into the above equation to solve for b.

Substitute (-4, 2) into the above equation.

2 = -3(-4)/4 + b

2 = -3(-1) + b

2 = 3 + b

Subtract 3 from both sides.

-1 = b

Substitute b = -1 in (1).

y = -3x/4 - 1

Multiply both sides by 4.

y = -3x/4 - 1

4(y) = 4(-3x/4 - 1)

4(y) = 4(-3x/4) + 4(-1)

4y = -3x - 4

Add 3x to both sides.

3x + 4y = -4

Add 4 to both sides.

3x + 4y + 4 = 0

7. Answer :

Equation of the line in slope-intercept form :

y = mx + b

Given : Slope is -2. So, substitute m = -2.

y = -2x + b ----(1)

Since the line passes through the point (4, -1) substitute the point (4, -1) into the above equation.

-1 = -2(4) + b

-1 = -8 + b

Add 8 to both sides.

7 = b

Substitute b = 7 in (1).

y = -2x + 7

Add 2x to both sides.

2x + y = 7

Subtract 7 from both sides.

2x + y - 7 = 0

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