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ehidna [41]
2 years ago
9

Determine the y intercept for the linear function 3x - 4y = 24. Show all work for credit.

Mathematics
2 answers:
klemol [59]2 years ago
8 0

Answer:

y-intercept = -6

Step-by-step explanation:

y-intercept is the value of "y" where a line meets the Y coordinate.

<u>The equation of the line</u>

The linear function given to us is a straight line of equation:

\boxed{\mathsf{3x-4y=24}}

We have two methods to determine the y intercept of the given line

<h3>Method #1</h3>

(Intercept form)

The intercept form will benefit us with not only the y-intercept but also the x-intercept.

If a line makes an x-intercept "a" and a y-intercept "b", it's equation in intercept form is given by:

\boxed{\mathsf{\frac{x}{a} +\frac{y}{b} =1}}    . . . . . . . .. . . (¡)

Our main motive here is to get a 1 on one side and have separate denominators for x and y.

<u>PROCESSING OUR CONVERSION:</u>

<u />=>\mathsf{3x-4y=24}<u />

<em>taking 24 to the denominator on the LHS:</em>

<em />\implies\mathsf{\frac{3x}{24} -\frac{4y}{24} =1}<em />

<em>reducing the fractions to their simplest form:</em>

<em />\implies\mathsf{\frac{x}{8} -\frac{y}{6}=1}<em />

<em>getting a plus in between the two fractions and taking the leftover minus to 6 of " </em>\frac{y}{6}"

<em />\implies\mathsf{\frac{x}{8} +\frac{y}{-6}=1}<em />

<em />

On comparing it with eqn. (¡), we get

a = 8 and b = -6

which are the x and y intercepts respectively

Since, the question's only asked for the y-intercept

<u>ANSWER:</u>

y-intercept = <u>- 6 </u>

<em>- - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - </em>

<h3>Method #2</h3>

(slope-intercept form)

The given equation is in standard form. To convert it into slope-intercept you simply have to isolate y.

<u>CONVERSION:</u>

\implies \mathsf{3x-4y=24}

<em>taking y to the RHS and getting 24 to the LHS</em>

<em>[NOTE: Signs change in doing so]</em>

<em />\implies \mathsf{3x-24=4y}<em />

<em>dividing both the sides by 4</em>

<em />\implies \mathsf{\frac{3x}{4} -6=y}<em />

<em />

This is the equation in slop-intercept form!

When a line meets the Y-axis it's x coordinate becomes 0.

[<em>Check the attachment</em>]

<em>Substituting x with 0</em>

<em />\implies \mathsf{0-6=y}<em />

<em />\implies \mathsf{-6=y}<em />

<em />

<u>ANSWER:</u>

x is 0 when y is -6.

Implies that the y intercept of the line is<u> -6 </u>

<u />

<u />

<u />

valina [46]2 years ago
7 0

Step-by-step explanation:

here is your answer hope you will enjoy and mark me as brainlist

thank you

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