Question

6. By midnight, a charity had collected 83 shirts. Every hour after that, it collected 20 more shirts. Let "h" be the number of hours since midnight and "n" be the number of shirts. Write a linear equation in slope-intercept form that relates the number of shirts collected and the number of hours since midnight.

7. The line containing the base of a right triangle has the equation y = 3x +4. The leg perpendicular to the base has an endpoint (6, 1). What is the slope-intercept form of the equation of the line containing the leg?

Answer 1

6) Equation that relates the number of hours and shirts is n = 20 h + 83.

7) The equation of line containing the leg is y = -(
`(1)/(3)`)x -1

Explanation:

Step 1 :

6)

Total number of shirts collected by midnight = 83

Number of shirts collected every hour = 20

Let h be number of hours after midnight and n be number of shirts collected

So the number of shirts collected for every hour h = 20h

Since 83 shirts are collected before midnight, the linear equation in slope intercept form to represent this would be

n = 20 h + 83.

Step 2 :

7)

Equation for the base of the triangle = y =3x +4

Slope of this line = 3

Slope of line perpendicular to this line = -(
`(1)/(3)`)

The endpoint of the leg perpendicular to the base is (6,1)

Hence the equation of this line is equation of line having slope as -(
`(1)/(3)`) and passing through (6,1)

(y -
`y_(1)`) = m (x -
`x_(1)`)

(y-1) = -(
`(1)/(3)`) (x-6)

y= -(
`(1)/(3)`)x + -(
`(1)/(3)`)6 + 1

=> y = -(
`(1)/(3)`)x -1

Step 4 :

Answer :

6) Equation that relates the number of hours and shirts is n = 20 h + 83.

7) Equation of line containing leg is y = -(
`(1)/(3)`)x - 1