Question

The equation of line v is y=9x+1. Line w is perpendicular to line v and passes through (3, – 2). What is the equation of line w?

Answer 1

Answer:

Step-by-step explanation:

Remember the general form of a linear equartion: y=mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0).

The equation of line v (y=9x+1) has a slope of 9. A perpendicular line with have a slope equal to the negative inverse of the reference line. So the line we want will have a slope of -(1/9). That gives us y = -(1/9)x + b. Any vale of b will produce a line that is perpendicular. But we want a line that goes through point (3,-2). All we need to do is find a value for b that will make that wish come true.

Use the point (3,-2) in y = -(1/9)x + b and solve for b:

y = -(1/9)x + b

-2 = -(1/9)*(3) + b

-2 = -(1/3) + b

b = - 1 2/3, or -(5/3)

The equation is y = -(1/9)x + - (5/3)

Answer 2

The equation of line w is $y+2=\frac{-1}{9} (x-3)$

Equation of a line

The equation of a line in point-slope form is expressed as:

• $y-y_1=\frac{-1}{m} (x-x_1)$

The slope of the line y = 9x + 1 is 9.

Substitute the slope m = 9, and the coordinate (3, -2) into the formula to have:

$y-(-2)=\frac{-1}{9} (x-3)\\y+2=\frac{-1}{9} (x-3)$

Hence the equation of line w is $y+2=\frac{-1}{9} (x-3)$

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