Question

Find the y intercept and x intercept of the line 2x+3y=-5

Answer 1

Lets write the equation in slope-intercept form

`y=mx+b,`

where m is the slope and b is the y-intercept.

Then, we have

`\begin{gathered} 3y=-5-2x \\ y=-(2)/(3)x-(5)/(3) \end{gathered}`

By comparing equations, we can note that the y-intercept is

`\begin{gathered} \\ b=-(5)/(3) \end{gathered}`

Now, the x-intercept occurs at y=0. By substituting this value into our line equation, we get

`0=-(2)/(3)x-(5)/(3)`

then, the x-intercept is given by

`\begin{gathered} -(2)/(3)x=(5)/(3) \\ x=-((5)/(3))/((2)/(3)) \\ x=-(5\cdot3)/(2\cdot3) \\ x=-(5)/(2) \end{gathered}`

Therefore, the answer is

- x intercept is -5/2

- y-intercept is -5/3