Question

Find the input value for the ordered pair (X, -22) if it is a point on the line with (-12, 6) and the line has a slope of m = 5/4

Answer 1

So, the input value for the ordered pair
`\((X, -22)\)`on the line with a slope of
`\(m = (5)/(4)\) is \(X = -(172)/(5)\).`

Explanation:

To find the input value (X) for the ordered pair (X, -22) if it is a point on the line with (-12, 6) and the line has a slope of
`\(m = (5)/(4)\)`, you can use the point-slope form of a linear equation:

`\(y - y_1 = m(x - x_1)\)`

Where:

`\(m\)`is the slope,

`\((x_1, y_1)\)`is a point on the line.

In this case, you have the point
`\((-12, 6)\)`and the slope
`\(m = (5)/(4)\).` You also have the point
`\((X, -22)\),` which you want to find.

Now, plug in the known values into the point-slope equation:

`\(y - 6 = (5)/(4)(x - (-12))\)`

Simplify:

`\(y - 6 = (5)/(4)(x + 12)\)`

Now, we want to find the input value
`\(X\)` when the output is -22, so set
`\(y\)` to -22:

`\(-22 - 6 = (5)/(4)(x + 12)\)`

Now, solve for
`\(x\)`:

`\(-28 = (5)/(4)(x + 12)\)`

To get rid of the fraction, multiply both sides by
`\((4)/(5)\)`:

`\((4)/(5) \cdot (-28) = x + 12\)`

`\(-(112)/(5) = x + 12\)`

Now, subtract 12 from both sides to isolate
`\(x\)`:

`\(x = -(112)/(5) - 12\)`

To find
`\(x\)`, you can calculate this expression:

`\(x = -(112)/(5) - (60)/(5) = -(172)/(5)\)`

So, the input value for the ordered pair
`\((X, -22)\)`on the line with a slope of
`\(m = (5)/(4)\) is \(X = -(172)/(5)\).`