Question

3) Find the equation, in standard form, of the line with a slope of -3 that goes through

the point (4, -1).

Answer 1

3x +y = 11

Explanation:

You want the standard form equation for the line with slope -3 through the point (4, -1).

Point-slope form

The point-slope form of the equation for a line with slope m through point (h, k) is ...

y -k = m(x -h)

For the given slope and point, the equation is ...

y -(-1) = -3(x -4)

y +1 = -3x +12

Standard form

The standard form equation of a line is ...

ax +by = c

where a, b, c are mutually prime integers, and a > 0.

Adding 3x -1 to the above equation gives ...

3x +y = 11 . . . . . . . . the standard form equation you want

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Additional comment

For a horizontal line, a=0 in the standard form. Then the value of b should be chosen to be positive.

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