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Finding the Intercepts of
To determine the intercepts of the equation , substitute zero for each variable in turn and solve for the other.
Finding the x-intercept: Set and solve for :
The x-intercept is the point (3, 0).
Finding the y-intercept: Set and solve for :
The y-intercept is the point .
The two intercepts of the line are (3, 0) and . Unlike equations where one variable has a coefficient of , here both intercept calculations require a division step — dividing by to find the x-intercept and dividing by to find the y-intercept. Dividing by the negative coefficient produces the negative y-intercept value .
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A logistics company uses the linear equation y = 500 - 20x to model the remaining balance (y) of a prepaid shipping account after x number of packages are sent. To find the x-intercept, which represents the total number of packages that can be sent before the balance reaches zero, which algebraic step must be performed?
A logistics company uses the linear equation y = 500 - 20x to model the remaining balance (y) of a prepaid shipping account after x number of packages are sent. To find the x-intercept, which represents the total number of packages that can be sent before the balance reaches zero, which algebraic step must be performed?
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A project analyst uses the linear equation 4x - 3y = 12 to model the relationship between labor hours (x) and material costs (y). When the analyst wants to find the intercepts (the points where the model meets the axes), which coordinates should be recorded for this specific equation?
A production manager uses the equation 4x - 3y = 12 to balance resource allocation between two assembly lines. When calculating the intercepts for this specific model, the manager identifies the x-intercept at (3, 0) and the y-intercept at (0, ____).
A business analyst is using the linear equation $4x - 3y = 12$ to model a cost constraint on a production graph. To ensure the model is graphed correctly, match each calculation component for this specific equation to its correct value or coordinate point as described in the training manual.
A logistics coordinator uses the linear equation 4x - 3y = 12 to model resource distribution. True or False: To find the y-intercept of this specific model, the coordinator must set x to zero and solve for y, which results in the coordinate point (0, 4).
A facilities manager uses the linear equation $4x - 3y = 12$ to model the floor space occupied by two types of storage racks. To determine the y-intercept for this specific model, arrange the following steps in the correct procedural order.
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A logistics coordinator uses the linear equation 4x - 3y = 12 to model the maximum capacity of a shipping route. To determine the x-intercept for this specific model, which coordinate point should be recorded in the system?
A site manager is using the linear equation to determine the boundary lines for a new equipment storage zone. To properly align the zone on a site map, the manager must identify the y-intercept of this specific equation. Which coordinate point should be recorded as the y-intercept?