Question

Find the slope and y-intercept for the graph of the equation
6x - 4y = -36

Answer 1

Refer to the attachment

Answer 2

`y = (3)/(2) x + 9`

Explanation:

We would like to write the given equation in slope intercept form of the line .

`\longrightarrow 6x - 4y = -36`

The slope intercept form of the line is
`y = mx + c` , where

• 
  `m` is the slope
• 
  `(x,y)` is a point on the line .
• 
  `c` is the y intercept .

we can rewrite the given equation as ,

`\longrightarrow 6x - 4y = -36 \\`

`\longrightarrow -4y = -36 -6x \\`

`\longrightarrow -4y = -6( x + 6)\\`

`\longrightarrow y =(-6)/(-4)(x + 6)\\`

`\longrightarrow y = (3)/(2)(x+6)\\`

`\longrightarrow y = (3)/(2)x +(3)/(2)* 6\\`

`\longrightarrow \underline{\underline{\pmb{ y =(3)/(2)x +9}}}{}`

This is the required equation of line in slope intercept form , with ;

• 
  `m = ( 3)/(2)`
• 
  `c = 9`