Question

Consider the following equation: −10x+3y=11-10x+3y=11 A) Write the above equation in the form y=mx+b.y=mx+b. Enter the values of mm and bb in the appropriate boxes below as integers or reduced fractions (in the form A/B.)

Answer 1

Given the equation of the line:

`-10x+3y=11`

A) You need to remember the Slope-Intercept Form of the equation of a line:

`y=mx+b`

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

Then, in order to write the equation, given in the exercise, in Slope-Intercept Form, you have to solve for the variable "y":

`\begin{gathered} 3y=10x+11 \\ \\ y=(10)/(3)x+(11)/(3) \end{gathered}`

Notice that in this case:

`\begin{gathered} m=(10)/(3) \\ \\ b=(11)/(3) \end{gathered}`

B) Given this value of "x":

`x=6`

You need to substitute it into the equation found in Part A, and then evaluate, in order to find the corresponding value of "y":

`\begin{gathered} y=(10)/(3)(6)+(11)/(3) \\ \\ y=(60)/(3)+(11)/(3) \\ \\ y=(60+11)/(3) \\ \\ y=(71)/(3) \end{gathered}`

Hence, the answers are:

A)

`y=(10)/(3)x+(11)/(3)`

B)

`(6,(71)/(3))`