Learn Before
Finding the Equation of a Line with Slope and -Intercept
To find the equation of a line when the slope and -intercept are given, substitute these values into the slope-intercept form, .
Step 1 — Identify the given values. The slope is and the -intercept is , meaning .
Step 2 — Substitute into the slope-intercept form. Replace with and with in the equation :
Step 3 — Simplify. Rewrite the addition of a negative as subtraction:
The equation of the line is . This procedure works because the slope-intercept form is a direct template for these two specific qualities of a line.
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Intermediate Algebra @ OpenStax
Ch.3 Graphs and Functions - Intermediate Algebra @ OpenStax
Algebra
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Learn After
A technician is monitoring the pressure in a cooling system. The pressure decreases at a constant rate of 9 units per hour, and the initial pressure at the start of the observation (hour 0) is 4 units below the reference baseline. If this relationship is modeled by a line with a slope of and a -intercept of , which equation correctly represents the pressure after hours?
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In a civil engineering project, a drainage pipe's elevation relative to a reference baseline is modeled by a linear equation. The pipe's elevation decreases at a constant rate of 9 units per horizontal meter (slope ). At the starting point (meter 0), the pipe's elevation is already 4 units below the reference baseline (-intercept of ). Match each component of this linear model to its correct mathematical representation.
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