Question

estimate the slope of the line.
find the slope of the line passing through the given points.

1. (2,3),(5,9)
2. (1,4),(3, - 2)
3. (-2,7),(-3, - 1)
4. (5, - 1),(-7,5)
5. (-11,0),(4, - 5)
6. (3,4),(0,0)

decide whether the line with the given slope rises, falls, is horizontal or is vertical.

1. m = 2
2. m = 0
3. m = - 7
4. m=\frac{2}{3}
5. m =-\frac{4}{5}
6. m is undefined.

tell whether the lines with the given slopes are parallel, perpendicular, or neither.

1. line 1: m = 2

line 2: m = - 2

1. line 1: m = 5

line 2: m=\frac{1}{5}

1. line 1: m =-\frac{3}{8}

line 2: m=\frac{8}{3}

1. line 1: m = 4

line 2: m = 4

1. line 1: m=\frac{1}{3}

line 2: m = - 3

1. line 1: m=\frac{2}{3}

line 2: m =-\frac{2}{3}

1. picking strawberries one afternoon your family goes out to pick strawberries. at 1:00 p.m., your family has picked 3 quarts. your family finishes picking at 3:00 p.m. and has 28 quarts of strawberries. at what rate was your family picking?
2. ramp the specifications of a ramp that leads onto a loading dock state that the slope of the ramp must be no steeper than \frac{1}{64}. if the ramp begins 200 feet from the base of the loading dock and the dock is 3 feet tall, does the ramps slope meet the specification?

Explanation:

4. Find the slope of the line passing through the points \((2,3)\) and \((5,9)\)

Step1: Recall slope - formula

The slope formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Here, \(x_1 = 2,y_1=3,x_2 = 5,y_2 = 9\).

Step2: Substitute values into formula

\(m=\frac{9 - 3}{5 - 2}=\frac{6}{3}=2\)

Step1: Analyze slope - sign

If the slope \(m>0\), the line rises from left to right. Since \(m = 2>0\), the line rises.

Step1: Check parallel condition

Two lines are parallel if \(m_1=m_2\). Here, \(2
eq - 2\), so they are not parallel.

Step2: Check perpendicular condition

Two lines are perpendicular if \(m_1\times m_2=-1\). Here, \(2\times(-2)=-4
eq - 1\), so they are not perpendicular.

Answer:

\(2\)

10. Decide whether the line with slope \(m = 2\) rises, falls, is horizontal, or is vertical