Question

write the equation of the line in standard form. slope of 2/3 and passing through the points (-5, 1)

Answer 1

Explanation:

The standard form of a linear equation is

`Ax+By=C`

However, it is a lot easier if we find the equation in slope-intercept form

`y=mx+b`

and then rearrange the above equation to write it in standard form.

We are told that the slope of the line is 2/3 which means m = 2/3; therefore, the above equation becomes

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

Moreover, fro the point (-5, 1) we know that when x = -5, then y = 1; therefore, the above equation gives

`1=(2)/(3)(-5)+b`

Simplifying the above gives

`1=-(10)/(3)+b`

adding 10/3 to both sides gives

`1+(10)/(3)=-(10)/(3)+b+(10)/(3)`
`\begin{gathered} (3)/(3)+(10)/(3)=b \\ \\ \end{gathered}`
`\therefore b=(13)/(3)`

With the value of b in hand, we write the slope-intercept of the equation:

`y=(2)/(3)x+(13)/(3)`

Now, to write the above in standard form, we multiply both sides by 3. This cancels out 3 in the denominator on the right-hand side and gives

`3y=2x+13`

Finally, subtracting 2x from both sides gives

`3y-2x=13`

Just shift the position of the terms on the left-hand the side and we get

`\boxed{-2x+3y=13.}`

which is the standard form of our equation!