Lesson 6 Point the Way Solidify Understanding

Ready

Make a graph of the function based on the following information. Then, write the explicit equation for the function.

1.

At $x = 0$ , the $y$ -value is $5$ . The $y$ -value decreases by $3$ units each time $x$ increases by $1$ .

Equation:

2.

At $x = 0$ , the $y$ -value is $16$ . The $y$ -value decreases by a factor of $\frac{1}{4}$ units each time $x$ increases by $1$ .

Equation:

3.

At $x = 0$ , the $y$ -value is $1$ . The $y$ -value increases by a factor of $10$ times each time $x$ increases by $1$ .

Equation:

4.

At $x = 0$ , the $y$ -value is $- 8$ . The $y$ -value increase by $2$ each time $x$ increases by $1$ .

Equation:

Set

Use the given information to create an explicit equation. Your explicit equation should be in either slope-intercept ( $y = m x + b$ ) or point-slope form ( $y = m (x - x_{1}) + y_{1}$ ). Use the form that is most efficient based on the given information.

5.

$m = - 7$ , $b = 4$

6.

$m = \frac{3}{8}$ , $b = - 3$

7.

$m = 16$ , $b = - \frac{1}{5}$

8.

$m = 9$ , $(0, - 7)$

9.

$m = \frac{2}{3}$ , $(- 6, 1)$

10.

$m = - 5$ , $(4, 11)$

For each table of values, write two different explicit equations in point-slope form.

11.

$x$	$y$
$32$	$17$
$33$	$11$
$34$	$5$
$35$	$- 1$

12.

$x$	$y$
$- 54$	$12$
$- 53$	$19$
$- 52$	$26$
$- 51$	$33$

13.

$x$	$y$
$21$	$43$
$22$	$34$
$23$	$25$
$24$	$16$

14.

For one of the tables in problems 11–13, show how the two equations you made in point-slope form are equivalent.

Go

Show that the right side of the equation is equivalent to the left side of the equation. Justify each of your steps. Use the example to help guide your work.

$\begin{aligned} Example: & Justification: \\ 2 x - 4 & = 8 + x - 5 x + 6 (x - 2) \\ = 8 - 4 x + 6 x - 12 & Add x - 5 x and distribute the 6 over (x - 2) \\ = - 4 + 2 x & Combine like terms. \\ 2 x - 4 & = 2 x - 4 & Commutative property of addition. \end{aligned}$

15.

$x - 5 = 5 x - 7 + 2 (3 x + 1) - 10 x$

16.

$6 - 13 x = 24 - 10 (2 x + 8) + 62 + 7 x$

17.

$14 x + 2 = 2 x - 3 (- 4 x - 5) - 13$