Answer:
[tex]y = \frac{1}{6}x - 4[/tex]
[tex]y = \frac{x}{2} + 2[/tex]
[tex]y = \frac{1}{8}x[/tex]
[tex]y = \frac{1}{6}x+ \frac{2}{3}[/tex]
[tex]y = 12x - 9[/tex]
Step-by-step explanation:
Required
Represent in gradient intercept form
This means that the equation be in form: [tex]y = mx + c[/tex]
Solving (a): [tex]3y = \frac{1}{2}x - 12[/tex]
Divide through by 3
[tex]\frac{3y}{3} = \frac{1}{3*2}x - \frac{12}{3}[/tex]
[tex]y = \frac{1}{6}x - 4[/tex]
Solving (b): [tex]5x = 10y - 20[/tex]
Make y the subject
[tex]10y = 5x + 20[/tex]
Divide through by 10
[tex]y = \frac{5x}{10} + \frac{20}{10}[/tex]
[tex]y = \frac{x}{2} + 2[/tex]
Solving (c): [tex]x = 8y[/tex]
Make y the subject
[tex]8y= x[/tex]
Divide through by 8
[tex]y = \frac{1}{8}x[/tex]
Solving (d): [tex]\frac{1}{2}x = 3y - 2[/tex]
Make y the subject
[tex]3y = \frac{1}{2}x+ 2[/tex]
Divide through by 3
[tex]y = \frac{1}{2*3}x+ \frac{2}{3}[/tex]
[tex]y = \frac{1}{6}x+ \frac{2}{3}[/tex]
Solving (d): [tex]\frac{2}{3}y - 8x = -6[/tex]
Make y the subject
[tex]\frac{2}{3}y = 8x -6[/tex]
Divide through by 3/2
[tex]\frac{3}{2} * \frac{2}{3}y =\frac{3}{2} * ( 8x -6)[/tex]
[tex]y =\frac{3}{2} * ( 8x -6)[/tex]
[tex]y =\frac{3}{2} * 8x -\frac{3}{2} * 6[/tex]
[tex]y = 3 * 4x - 3 * 3[/tex]
[tex]y = 12x - 9[/tex]
