A direct variation function contains the points (–8, –6) and (12, 9). Which equation represents the function?

Mathematics

1 answer:

mars1129 [50]3 years ago

6 0

Answer:

$y=\frac{3}{4}x$

Step-by-step explanation:

If it is a direct variation function, then $\frac{y}{x}=k$ .

$k$ can be found by choosing a point and doing $y$ divided by $x$ .

So we can find $k$ by doing -6 divided by -8 or 9 divided by 12.

Both of these values are equal to 0.75 or 3/4 as a fraction.

So you can say any point in this relation will follow the equation:

$\frac{y}{x}=\frac{3}{4}$

Multiply both sides by $x$ :

$y=\frac{3}{4}x$

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67. The line contains the point (4,0) and is parallel to the line defined by 3x = 2y.

olganol [36]

Answer:

$y=\frac{3}{2} x-6$

Step-by-step explanation:

Hi there!

What we need to know:

Linear equations are typically organized in slope-intercept form:

$y=mx+b$ where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)

Parallel lines will always have the same slope but different y-intercepts.

1) Determine the slope of the parallel line

Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.

$3x = 2y$

Switch the sides

$2y=3x$

Divide both sides by 2 to isolate y

$\frac{2y}{2} = \frac{3}{2} x\\y=\frac{3}{2} x$

Now that this equation is in slope-intercept form, we can easily identify that $\frac{3}{2}$ is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope $\frac{3}{2}$ . Plug this into $y=mx+b$ :