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":

$\begin{gathered} 3y=10x+11 \\ \\ y=\frac{10}{3}x+\frac{11}{3} \end{gathered}$

Notice that in this case:

$\begin{gathered} m=\frac{10}{3} \\ \\ b=\frac{11}{3} \end{gathered}$

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":

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

Hence, the answers are:

A)

$y=\frac{10}{3}x+\frac{11}{3}$

B)

$(6,\frac{71}{3})$