A technician is calibrating a sensor that follows a linear decline. The rate of change (slope) is -1/3, and the sensor must pass through a calibration point at (6, -4). Order the steps to find the sensor's linear equation in slope-intercept form (y = mx + b).

A financial analyst is modeling the depreciation of an asset. The value decreases at a constant rate of 1/3 thousand dollars per year (slope m = -1/3). At year 6, the asset's value relative to its starting point is -4 thousand dollars (point (6, -4)). According to the four-step procedure for finding the equation of a line, which of the following is the correct slope-intercept form?

Linear Modeling of Water Table Decline

A civil engineer is designing a drainage pipe with a constant downward slope of $m = -1/3$. The pipe must pass through a specific survey marker at the coordinates $(6, -4)$. Match each stage of the four-step procedure for finding the pipe's linear equation with its correct algebraic representation.

An operations manager is tracking a decline in production efficiency that follows a linear model with a slope of m = -1/3. The model passes through the point (6, -4). Following the four-step procedure to derive the final slope-intercept equation y = -1/3x + b, the value of the y-intercept (b) is ____.

An environmental consultant is modeling the rate of soil erosion, which has a constant slope of m = -1/3 inches per year. The model passes through a reference marker at coordinates (6, -4). True or False: According to the four-step procedure for finding the line's equation, the y-intercept (b) in the final slope-intercept form (y = mx + b) is positive 2.

Standard Operating Procedure: Documenting Linear Trends

Cooling System Efficiency Modeling

A field engineer is calculating the grade of a new drainage pipe. The design specifications require a slope of $m = -\frac{1}{3}$ and must pass through a survey point at $(6, -4)$. Which of the following equations correctly shows the first step of substituting these values into the point-slope formula, $y - y_1 = m(x - x_1)$, before any simplification is performed?

A field engineer is documenting the grade of a drainage pipe that has a constant slope of $m = -\frac{1}{3}$ and passes through a specific survey marker at the coordinates $(6, -4)$. While applying the standard four-step procedure, the engineer substitutes these values into the point-slope formula: $y - (-4) = -\frac{1}{3}(x - 6)$. According to the algebraic rules illustrated in this procedure, which of the following is the correct simplified form of the left side of the equation?