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

Sagot :

Answer:

y-intercept = -6

Step-by-step explanation:

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

The equation of the line

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

[tex]\boxed{\mathsf{3x-4y=24}}[/tex]

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

Method #1

(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:

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

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

PROCESSING OUR CONVERSION:

[tex]=>\mathsf{3x-4y=24}[/tex]

taking 24 to the denominator on the LHS:

[tex]\implies\mathsf{\frac{3x}{24} -\frac{4y}{24} =1}[/tex]

reducing the fractions to their simplest form:

[tex]\implies\mathsf{\frac{x}{8} -\frac{y}{6}=1}[/tex]

getting a plus in between the two fractions and taking the leftover minus to 6 of " [tex]\frac{y}{6}[/tex]"

[tex]\implies\mathsf{\frac{x}{8} +\frac{y}{-6}=1}[/tex]

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

ANSWER:

y-intercept = - 6

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Method #2

(slope-intercept form)

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

CONVERSION:

[tex]\implies \mathsf{3x-4y=24}[/tex]

taking y to the RHS and getting 24 to the LHS

[NOTE: Signs change in doing so]

[tex]\implies \mathsf{3x-24=4y}[/tex]

dividing both the sides by 4

[tex]\implies \mathsf{\frac{3x}{4} -6=y}[/tex]

This is the equation in slop-intercept form!

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

[Check the attachment]

Substituting x with 0

[tex]\implies \mathsf{0-6=y}[/tex]

[tex]\implies \mathsf{-6=y}[/tex]

ANSWER:

x is 0 when y is -6.

Implies that the y intercept of the line is -6

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