IDNLearn.com provides a collaborative environment for finding and sharing answers. Get accurate answers to your questions from our community of experts who are always ready to provide timely and relevant solutions.

A direct variation function contains the points [tex]\((-8,-6)\)[/tex] and [tex]\((12,9)\)[/tex]. Which equation represents the function?

A. [tex]\( y = -\frac{4}{3} x \)[/tex]
B. [tex]\( y = -\frac{3}{4} x \)[/tex]
C. [tex]\( y = \frac{3}{4} x \)[/tex]
D. [tex]\( y = \frac{4}{3} x \)[/tex]


Sagot :

To determine which equation represents the direct variation function that contains the points [tex]\((-8, -6)\)[/tex] and [tex]\( (12, 9) \)[/tex], we need to find the slope [tex]\( m \)[/tex] of the line that passes through these points.

1. We start by using the formula for the slope [tex]\( m \)[/tex] between two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex]:

[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]

2. Substituting the given points [tex]\((-8, -6)\)[/tex] and [tex]\( (12, 9) \)[/tex] into the slope formula:

[tex]\[ m = \frac{9 - (-6)}{12 - (-8)} \][/tex]

3. Simplify the numerator and the denominator:

[tex]\[ m = \frac{9 + 6}{12 + 8} = \frac{15}{20} \][/tex]

4. Simplify the fraction:

[tex]\[ m = \frac{15}{20} = \frac{3}{4} \][/tex]

5. Since a direct variation function has the form [tex]\( y = mx \)[/tex], where [tex]\( m \)[/tex] is the slope we just calculated, we now know that the equation representing the function is:

[tex]\[ y = \frac{3}{4} x \][/tex]

Among the provided choices, the correct equation is:
[tex]\[ y = \frac{3}{4} x \][/tex]

Therefore, the correct choice is:
[tex]\[ y = \frac{3}{4} x \][/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.