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
