1Cademy - Interpreting the Slope and h-Intercept of $$h = 2s + 50$$

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Slope-Intercept Form of an Equation of a Line

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Interpreting the Slope and h-Intercept of $h = 2s + 50$

The linear equation $h = 2s + 50$ serves as a real-world mathematical model estimating a woman's overall height in inches, $h$ , based directly on her shoe size, $s$ . Since the equation inherently fits the slope–intercept format, the assigned slope corresponds to the coefficient $2$ and the $h$ -intercept sits squarely at $(0, 50)$ .

ⓐ Estimate the height for a size $0$ shoe: Substitute $s = 0$ into the model: $h = 2(0) + 50 = 0 + 50 = 50$ inches.

ⓑ Estimate the height for a size $8$ shoe: Substitute $s = 8$ into the model: $h = 2(8) + 50 = 16 + 50 = 66$ inches.

ⓒ Interpret the slope and $h$ -intercept:

A slope equaling $2$ signifies that for each $1$ -size increment increase in shoe size ( $s$ ), the corresponding estimated height ( $h$ ) goes up by exactly $2$ inches.
The targeted $h$ -intercept of $(0, 50)$ dictates that given a theoretical female shoe size of precisely $0$ , the model conservatively estimates physical height at $50$ inches.

ⓓ Graph the equation: Since real-world dimensions far surpass basic numbering, select an optimally expanded grid for the coordinate axes. Initiate by plotting the baseline at the $h$ -intercept $(0, 50)$ . Processing the slope vertically as $\frac{2}{1}$ , trace a rise of $2$ units upward coupled to a run of $1$ unit to the right in order to map a valid secondary point at $(1, 52)$ . Rendering a continuous straight line that intercepts these coordinates maps out the model visually.

Updated 2026-04-23

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OpenStax Intermediate Algebra

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