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Here are a few recommended readings before getting started with this lesson.
Here are a few practice exercises before getting started with this lesson.
$x$ | $y=2x+1$ |
---|---|
$1$ | $3$ |
$2$ | A |
$3$ | B |
$4$ | $9$ |
$5$ | C |
Find the values of A, B, and C.
$x$ | $y=x+1$ |
---|---|
$-1$ | $0$ |
$0$ | $1$ |
$1$ | $2$ |
$2$ | $3$ |
$3$ | $4$ |
Consider now the following graphs.
Which of the graphs corresponds to the table?Direct variation, also known as direct proportionality or proportional relationship, occurs when two variables, $x$ and $y,$ have a relationship that forms a linear function passing through the origin where $x =0$ and $y =0.$
$y=kx$
$g$ | $0.5g$ | $p=0.5g$ |
---|---|---|
$0$ | $0.5(0)$ | $0$ |
$1$ | $0.5(1)$ | $0.5$ |
$2$ | $0.5(2)$ | $1$ |
$3$ | $0.5(3)$ | $1.5$ |
$4$ | $0.5(4)$ | $2$ |
Tadeo is given the following math homework.
Help Tadeo do his homework!The general form of a direct variation is $y=kx,$ where $k$ is the constant of variation.
Tearrik is given the graph of a direct variation and one of its points.
To complete his homework before going dancing, he wants to find the equation of the direct variation shown in the graph. Help him do this!The equation of a direct variation is $y=kx,$ where $k$ is the constant of variation.
This time, Tearrik is given the graph of a direct variation, but none of its points are plotted.
Once again, to complete his homework before going dancing, he wants to find the equation of the direct variation shown in the graph. Help him do this!Use any point on the line.
$x=-10$, $y=8$
$LHS/(-10)=RHS/(-10)$
Put minus sign in front of fraction
Calculate quotient
Rearrange equation
Find the constant of variation of the direct variation whose graph is given. If the answer is not an integer, write it as a decimal rounded to one decimal place.
$x$ | $x10 $ | $y=x10 $ |
---|---|---|
$1$ | $110 $ | $10$ |
$2$ | $210 $ | $5$ |
$3$ | $310 $ | $≈3.3$ |
$4$ | $410 $ | $2.5$ |
$5$ | $510 $ | $2$ |
$6$ | $610 $ | $≈1.7$ |
$7$ | $710 $ | $≈1.4$ |
$8$ | $810 $ | $1.25$ |
$9$ | $910 $ | $≈1.1$ |
$10$ | $1010 $ | $1$ |