Analytic Geometry

Lesson

Remember that every graph has an $X$`X`-axis and a $Y$`Y`-axis.

The numbers on the $X$`X`-axis are sometimes called the inputs, while the numbers on the $Y$`Y`-axis are called the outputs.

We're going to practice completing tables of inputs and outputs given a graph.

Given the following graph, fill in the table.

$X$X |
$2$2 | $4$4 | $6$6 | $8$8 | $10$10 | $12$12 | $14$14 | $16$16 |

$Y$Y |

Notice on the graph that when the input $X$`X` is $2$2, the output $Y$`Y` is $1$1.

We can fill this output in the table.

$X$X |
$2$2 | $4$4 | $6$6 | $8$8 | $10$10 | $12$12 | $14$14 | $16$16 |

$Y$Y |
$1$1 |

We can use this method to fill in the entire table like so.

$X$X |
$2$2 | $4$4 | $6$6 | $8$8 | $10$10 | $12$12 | $14$14 | $16$16 |

$Y$Y |
$1$1 | $2$2 | $3$3 | $4$4 | $5$5 | $6$6 | $7$7 | $8$8 |

Given the following graph, fill in the table.

Loading Graph...

$X$ `X`$1$1 $2$2 $3$3 $4$4 $Y$ `Y`$\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$

Buzz recorded his savings (in $dollars$`d``o``l``l``a``r``s`) over a few months in the graph given.

Loading Graph...

Fill in the table.

Months $1$1 $2$2 $3$3 $4$4 Savings $\editable{}$ $\editable{}$ $\editable{}$ $\editable{}$ Buzz estimates that he will have exactly $\$60$$60 in his savings by month $5$5. Is this true or false?

False

ATrue

BFalse

ATrue

B

Identify, through investigation with technology, the geometric significance of m and b in the equation y = mx + b