Question

Write an equation for the line in the given form.

slope is −5 and (6, 4) is on the line; standard form

Answer 1

5x +y = 34

Explanation:

Since a point and slope are given, it is convenient to start with point-slope form, then rearrange the equation to put it into standard form.

For slope m through point (h, k), the point-slope form of the equation of a line is usually written ...

y -k = m(x -h)

For m=-5 and (h, k) = (6, 4), the equation is ...

y -4 = -5(x -6)

y -4 = -5x +30 . . . . . eliminate parentheses

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Standard form looks like ...

ax + by = c

where a > 0 and GCD(a, b, c) = 1. Here's how we can get there.

5x +y -4 = 30 . . . . . . add 5x

5x +y = 34 . . . . . . . . . add 4 to get standard form.