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Find the $y$ -intercept of the line $12x + 16y = 6$ . Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

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Standard form: find x- and y-intercepts

Full solution

Q. Find the

y

-intercept of the line

12x + 16y = 6

. Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

Set $x$ to $0$ : To find the y-intercept of the line, we need to set $x$ to $0$ and solve for $y$ . $\newline$ Substitute $x = 0$ into the equation $12x + 16y = 6$ . $\newline$ $12(0) + 16y = 6$ $\newline$ $16y = 6$
Solve for y: Now, we divide both sides of the equation by $16$ to solve for $y$ . $\newline$ $\frac{16y}{16} = \frac{6}{16}$ $\newline$ $y = \frac{6}{16}$
Divide by $16$ : Simplify the fraction $\frac{6}{16}$ to its lowest terms. $\newline$ Both $6$ and $16$ are divisible by $2$ . $\newline$ $y = \left(\frac{6 \div 2}{16 \div 2}\right)$ $\newline$ $y = \frac{3}{8}$

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