GRAPHING LINES IN DIFFERENT FORMS

Graph the equation using any method.

Problem 1 :

6y = 3x + 6

Solution :

6y = 3x + 6

Divide each side by 6.

y = (3/6) x + (6/6)

y = (1/2) x + 1

The above equation is in the form y = mx + b

Then,

Slope (m) = 1/2

y-intercept = 1

Problem 2 :

-3 + x = 0

Solution :

-3 + x = 0

x = 3

Since x = 3 is a vertical line, there is no y-intercept and the slope is undefined.

Problem 3 :

4y = 16

Solution :

y = 4

y = 0x + 4

The above equation is in the form y = mx + b

Then,

Slope (m) = 0

y-intercept = 4

Problem 4 :

8y = -2x + 20

Solution :

To find x and y intercept we have to compare given equation with intercept form (x/a) + (y/b) = 1

2x + 8y = 20

Dividing by 20 on both sides,

(2x/20) + (8y/20) = 1

(x/10) + (2y/5) = 1

x -intercept (a) = 10

y -intercept (b) = 5/2

Problem 5 :

-4x = 8y + 12

Solution :

8y = -4x - 12

Divide each side by 8.

y = (-4/8) x - (12/8)

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

The above equation is in the form y = mx + b

Then,

Slope (m) = -1/2

y-intercept = -3/2

Problem 6 :

3.5x = 10.5

Solution :

3.5x = 10.5

x = 3

Since x = 3 is a vertical line, there is no y-intercept and the slope is undefined.

Problem 7 :

14 - 3x = 7y

Solution :

7y = -3x + 14

To find x and y intercept we have to compare given equation with intercept form (x/a) + (y/b) = 1

3x + 7y = 14

Dividing by 14 on both sides,

(3x/14) + (7y/14) = 1

(3x/14) + (y/2) = 1

x-intercept = 14/3

y-intercept = 2

Problem 8 :

2y - 5 = 0

Solution :

2y = 0x + 5

y = 5/2

The above equation is in the form y = mx + b

Then,

Slope (m) = 0

y-intercept = 5/2