Find the $y$-intercept and $x$-intercept of the line.

$-3 x+7 y=8$

$y$-intercept: $\square$

$x$-intercept: $\square$

To find the y -intercept, set x = 0 and solve for y : − 3 ( 0 ) + 7 y = 8 A rry = 7 8 ​ .
To find the x -intercept, set y = 0 and solve for x : − 3 x + 7 ( 0 ) = 8 A rr x = − 3 8 ​ .
The y -intercept is 7 8 ​ .
The x -intercept is − 3 8 ​ .
y − in t erce pt : 7 8 ​ , x − in t erce pt : − 3 8 ​ ​

Explanation

Understanding the Problem We are given the equation of a line: − 3 x + 7 y = 8 . Our goal is to find the y -intercept and the x -intercept of this line. The y -intercept is the point where the line crosses the y -axis, which occurs when x = 0 . The x -intercept is the point where the line crosses the x -axis, which occurs when y = 0 .

Finding the y-intercept To find the y -intercept, we substitute x = 0 into the equation of the line: − 3 ( 0 ) + 7 y = 8 0 + 7 y = 8 7 y = 8 y = 7 8 ​ So, the y -intercept is 7 8 ​ .

Finding the x-intercept To find the x -intercept, we substitute y = 0 into the equation of the line: − 3 x + 7 ( 0 ) = 8 − 3 x + 0 = 8 − 3 x = 8 x = − 3 8 ​ x = − 3 8 ​ So, the x -intercept is − 3 8 ​ .

Final Answer Therefore, the y -intercept is 7 8 ​ and the x -intercept is − 3 8 ​ .


Examples
Understanding intercepts is useful in many real-world scenarios. For example, if you are tracking the water level in a tank, the y-intercept might represent the initial water level, and the x-intercept could represent the time when the tank is empty. Similarly, in business, the y-intercept of a cost function could represent the fixed costs, and the x-intercept of a revenue function could represent the break-even point.

Answered by GinnyAnswer | 2025-07-05