Question

Enter the equation in slope intercept form. Then graph the line described by the equation. -6x-5y=10

Answer 1

`y=-(6)/(5)x-2`

Check the graph below, please

1) Since we have the equation in the Standard form we can manipulate it so that we can have the slope-intercept form:

`-6x-5y=10`

Let's isolate the y-term on the left:

`\begin{gathered} -6x-5y=10 \\ -5y=10+6x \\ (-5y)/(-5)=(10)/(-5)+(6x)/(-5) \\ y=-(6)/(5)x-2 \end{gathered}`

2) Now, let's plot the line of this function, by picking values for x and inserting them to get the value of y. We can write out the T table:

x|y

-1y=-6/5(-1)-2 => y=-0.8

0 | -2

1 |-3.2

With the points (-1, -0.8), (0,-2) and (1,-3.2) we can trace a decreasing line:

for the slope m is negative.

3) Hence, these are the answers above: