Question

What is the equation of the line described below written in slope-intercept form? the line passing through point (0, 0) and parallel to the line whose equation is 3x + 2y - 6 = 0 y = -x

Answer 1

y = -1½x + 3; Parallel Equation: y = -1½x [Direct Variation (y = mx)]

Explanation:

Set the equation equal to 6, move -3x to the right side of the equivalence symbol to get 2y = -3x + 6, then divide all terms by 2, to isolate the variable, resulting in y = -½x + 3. Now that we have our equation, we have to the PARALLEL equation [SIMILAR RATE OF CHANGES (SLOPES)] that passes through the origin [0, 0]. To do this, we simply plug these coordinates into the Slope-Intercept Formula, y = mx + b --> 0 = -½[0] + b. It is obvious that your y-intercept IS the origin [so as your x-intercept], so your parallel equation is y = -½x.

NOTE: The parent function of y = mx, is what is known as direct variation.