Question

Find the x and y intercepts of 2x-5y=12 (write all answers as points)

Answer 1

`\begin{gathered} x-\text{intercept is (6,0)} \\ y-\text{intercept is (}0,\text{ -}(12)/(5)) \end{gathered}`

Here, we want to find the x and y intercepts of the given line

We start by writing the equation of the line in the standard form

The standard form is;

`y\text{ = mx + b}`

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

We have the equation re-written as;

`\begin{gathered} 5y\text{ = 2x - 12} \\ y\text{ = }(2)/(5)x\text{ - }(12)/(5) \end{gathered}`

As we can see, we have the y-intercept at the point y = -12/5

The coordinate form at this point is (0,-12/5)

To find the x-intercept, we simply set y to zero

This is;

`\begin{gathered} 0\text{ = }(2)/(5)x\text{ - }(12)/(5) \\ \\ (2)/(5)x\text{ = }(12)/(5) \\ \\ 2x\text{ = 12} \\ x\text{ = }(12)/(2) \\ x\text{ = 6} \end{gathered}`

The x-intercept is thus (6,0)