algebra 2 practice

Question

Consider the line Li with equation y = 2x - 3.

The line L2 is parallel to L1 and passes through the point A(1,9).

The line L3 is perpendicular to L1 and passes through the point A(1,9).

1. Find the equation of the line L2
2. Find the equation of the line L3

The lines L1 and L3 intersect at point B

(c)

Find the coordinates of point B.

(d

Find the distance between the points A and B.

Answer 1

L2: 2=(y-9)/(x-1)

L3:-.5=(y-9)/(x-1)

Set the equation for L1=to the equation for 3 to show that the intersection is (5,7)

Use the distance formula to find the distance between A and B.

Answer 2

The slope for L3 is the negative reciprocal of the slope of either L1 or L2 (since both slopes are the same). So the slope of L3 is -1/2.

You can use either the slope-intercept form or the point-slope form of a linear equation to find the y-intercept.

y - y1 = m(x - x1) [point-slope form]

y-9 = (-1/2)(x-1)

y = (-1/2)x +1/2 + 9

y = (-1/2)x +9.5

Or

9 = (-1/2)(1) + b [y-intercept form)

9 = -0.5 + b

9.5 = b

Answer 3

Parallel lines share the same slope. Perpendicular lines have opposite, reciprocal slopes like 2 and -1/2 or 3/4 and -4/3.

y = mx + b

9 = 2(1) + b

9 = 2 + b

b = 7

y = 2x + 7 is the formula for L2.

The rest is on you. Go!