Example

Interpreting the Slope and CC-Intercept of C=1.8n+35C = 1.8n + 35

Loreen runs a calligraphy business. Her weekly cost is modeled by the linear equation C=1.8n+35C = 1.8n + 35, where CC is the weekly cost in dollars and nn is the number of wedding invitations she writes.

ⓐ Find CC when n=0n = 0: C=1.8(0)+35=0+35=35C = 1.8(0) + 35 = 0 + 35 = 35 Loreen's weekly cost is $35 when she writes 00 invitations.

ⓑ Find CC when n=75n = 75: C=1.8(75)+35=135+35=170C = 1.8(75) + 35 = 135 + 35 = 170 Her weekly cost is $170 when she writes 7575 invitations.

ⓒ Interpret the slope and CC-intercept:

  • The slope 1.81.8 means that the weekly cost increases by $1.80 for every additional invitation written.
  • The CC-intercept is (0,35)(0, 35), meaning her weekly cost is $35 even if 00 invitations are written.

ⓓ Graph the equation: To graph this equation, prepare a coordinate plane with a sufficiently large scale to fit the application's data. Start at the CC-intercept (0,35)(0, 35). By utilizing the slope 1.81.8 as an equivalent ratio (such as moving up 1818 units and right 1010 units, or multiplying to create larger integer steps), plot a second point. Draw a straight line passing through these points to visually represent the business cost model.

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Updated 2026-04-23

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