$-5x + 4y = -40$
x-intercept (?, ?)
y-intercept (?, ?)
Answer (1)
To find the x-intercept, set y = 0 and solve for x : − 5 x + 4 ( 0 ) = − 40 , so x = 8 . The x-intercept is ( 8 , 0 ) .
To find the y-intercept, set x = 0 and solve for y : − 5 ( 0 ) + 4 y = − 40 , so y = − 10 . The y-intercept is ( 0 , − 10 ) .
The x-intercept is 8 .
The y-intercept is − 10 .
Explanation
Understanding the Problem We are given the equation of a line: − 5 x + 4 y = − 40 . Our goal is to find the x-intercept and y-intercept of this line. The x-intercept is the point where the line crosses the x-axis, meaning y = 0 . The y-intercept is the point where the line crosses the y-axis, meaning x = 0 .
Finding the x-intercept To find the x-intercept, we substitute y = 0 into the equation − 5 x + 4 y = − 40 and solve for x .
Substituting y=0 Substituting y = 0 , the equation becomes − 5 x + 4 ( 0 ) = − 40 , which simplifies to − 5 x = − 40 .
Solving for x Now, we solve for x : x = − 5 − 40 = 8 Thus, the x-intercept is ( 8 , 0 ) .
Finding the y-intercept To find the y-intercept, we substitute x = 0 into the equation − 5 x + 4 y = − 40 and solve for y .
Substituting x=0 Substituting x = 0 , the equation becomes − 5 ( 0 ) + 4 y = − 40 , which simplifies to 4 y = − 40 .
Solving for y Now, we solve for y : y = 4 − 40 = − 10 Thus, the y-intercept is ( 0 , − 10 ) .
Final Answer Therefore, the x-intercept is ( 8 , 0 ) and the y-intercept is ( 0 , − 10 ) .
Examples
Understanding intercepts is crucial in various real-world applications. For instance, in economics, the x-intercept of a supply curve can represent the minimum price at which a seller is willing to supply a product, while the y-intercept of a demand curve can indicate the maximum price a consumer is willing to pay. Similarly, in physics, intercepts can represent initial conditions or boundary values in equations describing motion or other phenomena. Knowing how to find and interpret intercepts allows us to analyze and make predictions about these real-world scenarios.
