Question

write an equation of the line that satisfies the given conditions. give the equation (a) in slope intercept form and (b) in standard form. m=-7/12 ,(-6,12)

Answer 1

Given the slope of the line:

`m=-(7)/(12)`

And this point on the line:

`(-6,12)`

(a) By definition, the Slope-Intercept Form of the equation of a line is:

`y=mx+b`

Where "m" is the slope and "b" is the y-intercept.

In this case, you can substitute the slope and the coordinates of the known point into that equation, and then solve for "b", in order to find the y-intercept:

`12=(-(7)/(12))(-6)+b`
`12=(42)/(12)+b`
`\begin{gathered} 12=(42)/(12)+b \\ \\ 12=(7)/(2)+b \end{gathered}`
`\begin{gathered} 12-(7)/(2)=b \\ \\ b=(17)/(2) \end{gathered}`

Therefore, the equation of this line in Slope-Intercept Form is:

`y=-(7)/(12)x+(17)/(2)`

(b) The Standard Form of the equation of a line is:

`Ax+By=C`

Where A, B, and C are integers, and A is positive.

In this case, you need to add this term to both sides of the equation found in Part (a), in order to rewrite it in Standard Form:

`(7)/(12)x`

Then, you get:

`(7)/(12)x+y=(17)/(2)`

Hence, the answers are:

(a) Slope-Intercept Form:

`y=-(7)/(12)x+(17)/(2)`

(b) Standard Form:

`(7)/(12)x+y=(17)/(2)`