Write an equation of the line that contains the point (3.-2) and is perpendicular to the line 3x - 6y = 7.

y = -2x + 4

Step-by-step explanation:

Perpendicular lines intersect at a point that form right angles; these lines also have negative reciprocal slopes, in which the product of their slopes result in a negative one (-1 ).  

Given the linear equation in standard form, 3x - 6y = 7, and the point (3, -2):

Transform the standard form into slope-intercept form: y = mx + b

3x - 6y = 7

3x - 3x - 6y = -3x + 7

-6y = -3x + 7

Divide both sides by -6 to isolate y:

y = ½x - 7/6  (This is the slope-intercept form of the given equation,  3x - 6y = 7).

Now that we have the slope of the given equation, = ½, then we can determine that the slope of the other line must be =  -2:

× =  ½ × -2 = -1

Next, using the slope of the other line, =  -2, and the given point, (3, -2), substitute these values into the slope-intercept form to solve for the value of the y-intercept, b:

y = mx + b

-2 = -2(3) + b

-2 = -6 + b

Add 6 to both sides to isolate b:

-2 + 6 = -6 + 6 + b

4 = b  (This is the y-intercept of the other line).

Therefore, the linear equation of the line that is perpendicular to 3x - 6y = 7 is:

step-by-step explanation:

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