Question

Select the equation of a line in slope-intercept form that passes through (–2, 2) and is perpendicular to the graph of y = 1/2x-3

Answer 1

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Answer 2

Given,

A line passes through (–2, 2) and is perpendicular to the graph of y = 1/2x-3.

To find,

Find the equation of the line.

Solution,

• Let, the coordinates of the line be ( X, Y ).

• The line is perpendicular to y = (1/2)x - 3.

• The slope m1 of line y = (1/2)x - 3 is (1/2) because it is of the form of y=mx +c, where m is the slope of the line and c is constant.

• The line y = (1/2)x - 3 is perpendicular to the required line.

• The product of slopes of two perpendicular lines m1 and m2 is -1.

           ⇒m1 × m2 = -1.

           ⇒(1/2) × m2 = -1.

           ⇒m2 = -2.

• The slope of the required equation of the line is -2.

• The required line passes through (-2,2).

• Further solving by applying formula : (Y-A)/(Y-B)= m2

          ⇒ (Y-2/X+2)=-2

          ⇒ Y - 2 = -2X -4.

           ⇒Y + 2X + 4 - 2 = 0

           ⇒2X + Y +2 = 0

Hence, the equation of a line in slope-intercept form that passes through (–2, 2) and is perpendicular to the graph of y = 1/2x-3 is 2X + Y +2 = 0