Question

Write an equation of the line that passes through the pair of points. Leave in simplest fractional form. (9, 2), (-2, 6)

Answer 1

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To find the equation of the line passing through the points
`\bf\:(9, 2)` and
`\bf\:-2, 6)`, we first need to calculate the slope
`\bf\:m` using the formula:

`\sf\rightarrow\:m = (y_2 - y_1)/(x_2 - x_1)\\`

where
`\sf\:(x_1, y_1) = (9, 2) and (x_2, y_2) = (-2, 6)`.

`\sf\rightarrow\:m = (6 - 2)/(-2 - 9) = (4)/(-11)\\`

Now that we have the slope
`\sf\:m = (4)/(-11)`, we can use the point-slope form of the equation of a line:

`\sf\rightarrow\:y - y_1 = m(x - x_1)\\`

Substituting
`\sf\:(x_1, y_1) = (9, 2)` and
`\sf\:m = (4)/(-11)` into the equation, we get:

`\sf\rightarrow\:y - 2 = (4)/(-11)(x - 9)`

To simplify this equation, first, distribute
`\bf\:(4)/(-11)` into
`\bf\:(x - 9)`:

`\sf\rightarrow\:y - 2 = (4)/(-11)x + (36)/(11)`

Next, bring
`\bf\:-2` to the right-hand side by adding
`\bf\:2` to both sides of the equation:

`\sf\rightarrow\:y = (4)/(-11)x + (36)/(11) + 2\\`

Now, simplify the equation further:

`\sf\rightarrow\:y = (4)/(-11)x + (36)/(11) + (22)/(11)\\`

`\sf\rightarrow\:y = (4)/(-11)x + (58)/(11)\\`

Therefore, the equation of the line passing through
`\bf\:(9, 2)` and
`\bf\:(-2, 6)` in simplest fractional form is:

`\textrm\displaystyle\sf y = (4)/(-11)x + (58)/(11)`

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