Question

Instructions: Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Match each linear equation with its slope and a point on the line.

Tiles:

slope= 3, point= (2,17)

slope= 1/3, point= (19,2)

slope= 3, point= (5,2)

slope= 1/3, point= (17,-2)

slope= 1/3, point= (-5,2)


Pairs:

y=3x-13

y=3x+11

3y=x+11

3y=x-13

Answer 1

y=3x-13 : slope = 3, point = (5, 2)

y=3x+11 : slope = 1/3, point = (-5, 2)

3y=x+11 : slope = 3, point = (2,17)

3y=x-13 : slope = 1/3, point = (19, 2)

Explanation:

Since, the equation of a line passes through
`(x_1, y_1)` with slope m is,

`y-y_1=m(x-x_1)`

If m = 3,
`x_1=2`,
`y_1=17`

Equation of the line,

`y-17=3(x-2)`

`y-17=3x-6`

`y = 3x - 6 + 17\implies y = 3x + 11`

If m = 1/3,
`x_1=19`,
`y_1=2`

Equation of the line,

`y-2=(1)/(3)(x-19)`

`3y-6=x-19`

`3y = x-19+6\implies 3y = x -13`

If m = 3,
`x_1=5`,
`y_1=2`

Equation of the line,

`y-2=3(x-5)`

`y-2=3x-15`

`y = 3x - 15 + 2\implies y = 3x -13`

If m = 1/3,
`x_1=17`,
`y_1=-2`

Equation of the line,

`y+2=(1)/(3)(x-17)`

`3y+6=x-17`

`3y=x-17-6\implies 3y = x-23`

If m = 1/3,
`x_1=-5`,
`y_1=2`

Equation of the line,

`y-2=(1)/(3)(x+5)`

`3y-6=x+5`

`3y=x+5+6\implies 3y = x+11`

Answer 2

y = 3x - 13................slope= 3, point= (5,2)

y = 3x + 11.................slope= 3, point= (2,17)

3y = x + 11................slope= 1/3, point= (-5,2)

3y = x - 13................slope= 1/3, point= (19,2)

Explanation:

To match each equation to its slope and point, remember that an equation in y = mx + b has slope m. The point must also satisfy or make true the equation when substituted for (x,y).

y=3x-13 has slope 3. The point (2,17) make it false. But (5,2) makes it true.

17 = 3(2) - 13 2 = 3(5) - 13

17 = 6-13 2 = 15 - 13

17 = - 7 False 2 = 2 True

y=3x+11 has slope 3. This means (2,17) must be true.

3y=x+11 can be converted to y = 1/3x + 11/3. It has slope 1/3. Test each point.

2= 1/3(19) + 11/3 -2 = 1/3(17) + 11/3 2 = 1/3(-5) + 11/3

2 = 19/3 + 11/3 -2 = 17/3 + 11/3 2 = -5/3 + 11/3

False False 2 = 6/3 True

3y=x-13 can be converted to y = 1/3x - 13/3. It has slope 1/3. Test each remaining point.

2= 1/3(19) - 13/3 -2 = 1/3(17) - 13/3

2 = 19/3 - 13/3 -2 = 17/3 - 13/3

2 = 6/3 -2 = 4/3

True False