Question

Help please

through the given point and perpendicular to the given equation write your answer in slope intercept form

1) ( -4 , 2) and 6x - y = 1

2) ( -3 , -5) and y = - x + 3

3) ( 1 , 4 ) and y = 1/2 x + 4

Answer 1

1. y = (-1/6)x +4/3
2. y = x -2
3. y = -2x +6

Explanation:

A simple, mechanical way to do these (perpendicular lines) is ...

• replace any constant with 0
• swap the x- and y-coefficients, negating one
• for point (h, k), replace x with (x-h) and y with (y-k)
• solve for y (to get slope-intercept form)

1) (x+4) +6(y -2) = 0 . . . .after step 3 above

... x -8 = -6y . . . . . . . . . . eliminate parentheses, add the opposite of the y-term

... y = (-1/6)x +4/3 . . . . . divide by the y-coefficient

2) (y+5) = (x +3)

... y = x -2 . . . . . . . . . . . . . add -5

3) (1/2)(y -4) = -(x -1)

... 1/2y -2 = -x +1 . . . . . . . eliminate parentheses

... 1/2y = -x +3 . . . . . . . . . add 2

... y = -2x +6 . . . . . . . . . . . multiply by 2

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Comment on the graph(s)

The attached graphs show the original lines and points (1: red, 2: blue, 3: green). The original line is dashed, and the perpendicular line through the point is shown solid. This confirms the results above.