Learn Before
Finding the Equation of a Line with Slope and -Intercept
To formulate the equation of a line given its slope and -intercept, substitute the specific values straight into the general slope-intercept form, .
Given: slope and -intercept .
Step 1 — Identify the components. As given, the slope and the intercept value .
Step 2 — Substitute into the formula.
Step 3 — Simplify the resulting expression. Write simply as and translate the addition of a negative value into subtraction:
The correct equation of the line is . This emphasizes taking care to correctly simplify negative coefficients and constants in final linear models.
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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A facility manager uses the equation y = 0.15x + 500 to calculate the monthly electricity bill (y) based on the number of kilowatt-hours used (x). In this slope-intercept form equation, which value represents the y-intercept, indicating the fixed monthly service charge?
A service technician uses the equation y = 45x + 75 to determine the total cost (y) of a repair based on the number of hours worked (x). In the standard slope-intercept form y = mx + b, the letter ____ represents the y-intercept, which in this scenario is the 75 dollar flat fee for the service call.
A freelance graphic designer uses the slope-intercept form equation y = 60x + 100 to calculate the total cost (y) for a project based on the number of hours worked (x). Match each part of the slope-intercept formula y = mx + b to its specific role in this business calculation.
A logistics coordinator uses the equation to calculate shipping costs. In the standard slope-intercept form , the y-intercept is always represented by the ordered pair (b, 0).
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A business consultant is explaining the structure of a linear cost model to a client using the slope-intercept form (). Arrange the following components in the correct sequence as they appear in the standard mathematical equation from left to right.
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A human resources manager uses the slope-intercept form, , to model an employee's salary growth. If represents the total annual salary and represents the number of years with the company, which variable in the equation represents the slope, indicating the constant dollar amount the salary increases each year?
A corporate data analyst is documenting a linear growth model for a team report using the slope-intercept form (). To ensure precise communication, match each algebraic component to its correct mathematical description.
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Learn After
A quality control technician is monitoring the calibration of a sensor. The sensor's accuracy is drifting downward at a rate of 1 unit per month (slope ). At the start of the monitoring period, the sensor is already 3 units below the standard calibration point (represented by a -intercept of ). Which linear equation correctly models this calibration drift over months in slope-intercept form?
A property manager is tracking the value of an appliance that depreciates at a constant rate. The value decreases by 1 unit per year (slope ) and started with an initial valuation adjustment of -3 units (-intercept (0, -3)). Arrange the following steps in the correct order to determine the simplified linear equation in slope-intercept form.
An environmental safety officer is monitoring a containment pit where the water level is currently 3 meters below the safety line (represented by the -intercept ). The level is dropping at a rate of 1 meter per hour (slope ). Match each component of the linear model for this situation with its correct numerical value or simplified expression.
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A logistics coordinator is tracking a supply chain deficit. The deficit is growing at a constant rate of 1 unit per day, but to model this as a reduction in available stock, the slope is defined as . The initial state is already 3 units below the target safety stock, which is represented by the -intercept . In the slope-intercept form , the simplified equation that models this inventory level after days is ____.
A retail department manager is setting up a digital tracking spreadsheet to monitor a promotional store account that began with a deficit of 3 units (where each unit represents 1,000 dollars, giving a -intercept of ). Due to a weekly service fee, the account balance decreases by 1 unit per week (representing a constant rate of change or slope of ).
True or False: To model this projected balance after weeks, the manager can correctly formulate this linear relationship
Agricultural Silo Linear Modeling