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Find the $y$ -intercept of the line $y = \frac{4}{3}x + \frac{2}{3}$ . Write your answer as an integer or as a simplified proper or improper fraction, not as an ordered pair.

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Slope-intercept form: find the slope and y-intercept

Full solution

Q. Find the

y

-intercept of the line

y = \frac{4}{3}x + \frac{2}{3}

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

Definition of y-intercept: The $y$ -intercept of a line is the point where the line crosses the $y$ -axis. This occurs when the $x$ -value is $0$ .
Substitute $x = 0$ : To find the y-intercept, we substitute $x = 0$ into the equation $y = \frac{4}{3}x + \frac{2}{3}$ .
Calculate y value: Substituting $x = 0$ gives us $y = \frac{4}{3}(0) + \frac{2}{3}$ .
Final result: Simplifying the equation, we get $y = 0 + \frac{2}{3}$ , which means $y = \frac{2}{3}$ .

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