Question

Sara is trying to find an equation for a line that passes through (5, 2) and is perpendicular to 3x + 2y = 15. Explain the steps that Sara could take to determine the equation. A) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the slope of that line and the point (5, 2) into the point-slope formula. B) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. C) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (5, 2) into the point-slope formula. D) Write 3x + 2y = 15 in slope-intercept form. Then, substitute the opposite reciprocal of the slope of that line and the point (0, 0) into the point-slope formula.

Answer 1

Not on your list, but an easy way is
.. a) swap coefficients of x and y, negating one. (Now you have 2x -3y.)
.. b) set any constant term to zero (now you have 2x -3y = 0)
.. c) translate the line to the point (5, 2) by substituting x ⇒ x-5, y⇒ y-2
2(x -5) -3(y -2) = 0


The way you've been taught, selection C is the proper choice.