$x+4 y=-56$
x-intercept ([?], $\square$)
y-intercept ($\square$, )
Answer (1)
To find the x-intercept, set y = 0 and solve for x : x = − 56 , so the x-intercept is ( − 56 , 0 ) .
To find the y-intercept, set x = 0 and solve for y : 4 y = − 56 , so y = − 14 , and the y-intercept is ( 0 , − 14 ) .
The x-intercept is ( − 56 , 0 ) .
The y-intercept is ( 0 , − 14 ) .
Explanation
Understanding the Problem We are given the equation of a line: x + 4 y = − 56 . Our goal is to find the x-intercept and the y-intercept of this line. The x-intercept is the point where the line crosses the x-axis, which means y = 0 . The y-intercept is the point where the line crosses the y-axis, which means x = 0 .
Finding the x-intercept To find the x-intercept, we substitute y = 0 into the equation x + 4 y = − 56 :
x + 4 ( 0 ) = − 56 x + 0 = − 56 x = − 56 So, the x-intercept is the point ( − 56 , 0 ) .
Finding the y-intercept To find the y-intercept, we substitute x = 0 into the equation x + 4 y = − 56 :
0 + 4 y = − 56 4 y = − 56 y = 4 − 56 y = − 14 So, the y-intercept is the point ( 0 , − 14 ) .
Final Answer Therefore, the x-intercept is ( − 56 , 0 ) and the y-intercept is ( 0 , − 14 ) .
Examples
Understanding intercepts is crucial in various real-world applications. For example, in economics, if the equation represents a budget constraint, the intercepts show the maximum amount of one good you can buy if you spend all your money on it. Similarly, in physics, if the equation represents the motion of an object, the intercepts can represent the initial position or the time when the object reaches a certain point. Knowing how to find intercepts helps in interpreting and analyzing such relationships.
