Question

Line A passes through the points (−3, 2) and (−23, 54). Line B is parallel to line A and passes through the point (−8, 0). What is the equation of line B?

A 30° central angle in a circle is equivalent to π/6 radians. The length of the arc intercepted by this central angle is ____ times the length of the radius.

a) 3π
b) 2π
c) π/2
d) 3

Answer 1

To find the equation of line B, we can use the slope-intercept form of a line. We find the slope by using the coordinates of line A, which is also the slope of line B since they are parallel. Then, using the slope and a point on line B, we can find the equation.

Step-by-step explanation:

To find the equation of line B, we first need to find its slope. Since line B is parallel to line A, it will have the same slope as line A. The formula to find the slope is (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are any two points on the line. Let's take the coordinates of (−3, 2) and (−23, 54) to calculate the slope:

Slope = (54 - 2) / (-23 - (-3)) = 52 / -20 = -2.6

Now, we can use the point-slope form of a line, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line. We'll use the point (-8, 0) as (x1, y1) and the slope we just calculated (-2.6) to find the equation of line B:

y - 0 = -2.6(x - (-8))

y = -2.6x + 20.8