Question

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

Answer 1

Answer:

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)

Step-by-step 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                        

Answer 2

Answer:

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)

Step-by-step 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,

$y-2=\frac{1}{3}(x-19)$

$3y-6=x-19$

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

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,

$y+2=\frac{1}{3}(x-17)$

$3y+6=x-17$

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

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

Equation of the line,

$y-2=\frac{1}{3}(x+5)$

$3y-6=x+5$

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