Question

Jordan is building a backyard deck. In the blueprints, the left side of the deck is perpendicular to its front side. Select all the choices that could represent the equation of the front side if the left side's equation is 3x-2y=10.

a) 2x+3y = 12
b) 3x + 2y = 12
c) -2x + 3y = -10
d) -3x + 2y = -10

Answer 1

The question is about finding the equations of a line perpendicular to a given line in a geometrical context. The correct equations for the front side of the deck, perpendicular to the left side, are a) 2x + 3y = 12 and d) -3x + 2y = -10.

Step-by-step explanation:

The subject of this question is Mathematics, and it relates to the concept of linear equations and perpendicular lines in geometry. The left side of Jordan's backyard deck is represented by the equation 3x - 2y = 10.

Since the front side is perpendicular to the left side, we are looking for an equation whose slope is the negative reciprocal of the slope of the left side's equation.

The slope of the left side's equation is 3/2 (after rearranging the equation to y = mx + b format), so the slope of a line perpendicular to it would be -2/3.

Therefore, the equations representing the front side of the deck could be a) 2x + 3y = 12 and d) -3x + 2y = -10, both of which have a slope of -2/3 when converted to the slope-intercept form.