Find the x-intercept and y-intercept of the following linear equation:
[tex]$-7 x+4 y=56$[/tex]
x-intercept (?, ?)
y-intercept (?, ?)
Answer (2)
To find the x-intercept, substitute y = 0 into the equation and solve for x . The x-intercept is ( − 8 , 0 ) .
To find the y-intercept, substitute x = 0 into the equation and solve for y . The y-intercept is ( 0 , 14 ) .
The x-intercept is ( − 8 , 0 ) .
The y-intercept is ( 0 , 14 ) .
Explanation
Understanding the Problem We are given the linear equation − 7 x + 4 y = 56 and asked to find the x-intercept and y-intercept. 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 − 7 x + 4 y = 56 :
− 7 x + 4 ( 0 ) = 56 − 7 x = 56 x = − 7 56 x = − 8 So the x-intercept is ( − 8 , 0 ) .
Finding the y-intercept To find the y-intercept, we substitute x = 0 into the equation − 7 x + 4 y = 56 :
− 7 ( 0 ) + 4 y = 56 4 y = 56 y = 4 56 y = 14 So the y-intercept is ( 0 , 14 ) .
Final Answer Therefore, the x-intercept is ( − 8 , 0 ) and the y-intercept is ( 0 , 14 ) .
Examples
Understanding intercepts is crucial in various real-world applications. For instance, in economics, the x-intercept of a cost function can represent the break-even point, where costs equal revenue. Similarly, in physics, intercepts can indicate initial conditions or points of equilibrium. Knowing how to find intercepts helps in analyzing and interpreting linear relationships in diverse fields.
The x-intercept of the equation − 7 x + 4 y = 56 is ( − 8 , 0 ) , and the y-intercept is ( 0 , 14 ) .
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