Question

Find the equation in standard form of the line with slope (-4/3) that passes through the point (4, 6).

(A) (3x + 4y = 24)
(B) (4x - 3y = -18)
(C) (3x - 4y = -6)
(D) (4x + 3y = 18)

Answer 1

The equation in standard form of the line with slope -4/3 that passes through the point (4, 6) is 4x + 3y = 34. Finally, converting to standard form, we obtain 4x + 3y = 34.

Step-by-step explanation:

To find the equation of a line in standard form, we need the slope and a point on the line.

Given the slope m = -4/3 and the point (4, 6), we can use the point-slope form of a linear equation: y - y1 = m(x - x1).

Substituting the values, we get y - 6 = (-4/3)(x - 4).

Expanding and rearranging the equation, we get 3y - 18 = -4x + 16.

Finally, converting to standard form, we obtain 4x + 3y = 34.