Question

Match each pair of points to the equation of the line that is parallel to the line passing through the points.

Answer 1

Answer: Below, see BOTH pictures

Step-by-step explanation: Filler Text

It was learned earlier in Lesson 3 that the slope of the line on a position versus time graph is equal to the velocity of the object. If the object is moving with a velocity of +4 m/s, then the slope of the line will be +4 m/s. If the object is moving with a velocity of -8 m/s, then the slope of the line will be -8 m/s. If the object has a velocity of 0 m/s, then the slope of the line will be 0 m/s. The slope of the line on a position versus time graph tells it all. Because of its importance, a student of physics must have a good understanding of how to calculate the slope of a line. In this part of the lesson, the method for determining the slope of a line on a position-time graph will be discussed.

The slope equation says that the slope of a line is found by determining the amount of rise of the line between any two points divided by the amount of run of the line between the same two points. In other words,

Pick two points on the line and determine their coordinates.

Determine the difference in y-coordinates of these two points (rise).

Determine the difference in x-coordinates for these two points (run).

Divide the difference in y-coordinates by the difference in x-coordinates (rise/run or slope).

The diagram below shows this method being applied to determine the slope of the line. Note that three different calculations are performed for three different sets of two points on the line.

Answer 2

`B(5,2) \:\: C(7,-5) \:\: \rightarrow y=-3.5x-15`

`D(11,6)\:\: E(5,9)\:\: \rightarrow y=-0.5x-3`

`H(4,4)\:\: I(8,9) \:\: \rightarrow y=1.25x+4`

`L(5,-7)\:\: M(4,-12)\:\: \rightarrow y=5x+9`

Explanation:

We need to match the slope of the function with the slope of the lines connecting the two points given. The slope of the lines are as follows:

`B(5,2) \:\: C(7,-5)=(2--5)/(5-7) =-3.5`

`D(11,6)\:\: E(5,9)=(6-9)/(11-5) =-0.5`

`H(4,4)\:\: I(8,9)=(4-9)/(4-8) =1.25`

`L(5,-7)\:\: M(4,-12)=(-7--12)/(5-4) =5`

`F(-7,12)\:\: G(3,-8)=(12--8)/(-7-3)=-2`

`J(7,2)\:\:K(-9,8) =(2-8)/(7--9) =-0.375`

Now,

the slope of the line BC matches with the slope of y=-3.5x-15.

the slope of the line DE matches with the slope of y=-0.5x-3.

the slope of the line HI matches with the slope of y=1.25x+4.

the slope of the line LM matches with the slope of y=5x+9.

and the slopes of the lines FG and JK do not match with any of the functions given.

Thus,

`B(5,2) \:\: C(7,-5) \:\: \rightarrow y=-3.5x-15`

`D(11,6)\:\: E(5,9)\:\: \rightarrow y=-0.5x-3`

`H(4,4)\:\: I(8,9) \:\: \rightarrow y=1.25x+4`

`L(5,-7)\:\: M(4,-12)\:\: \rightarrow y=5x+9`