Mathematics · Ch 5 — Straight Line

Slope-Intercept Form

5.3.2

Slope-Intercept Form

5.3.2 Slope-Intercept Form

Goal. Find the equation of the line with slope $m$ that makes Y-intercept $c$ .

Proof. The line meets the Y-axis at $C(0,c)$ . For any other point $P(x,y)$ on the line, the slope computed between $C$ and $P$ is $\dfrac{y-c}{x-0}$ , which must equal $m$ :

\frac{y-c}{x} = m \implies y = mx + c.

This is the well-known slope-intercept form. …

Figure 5.3.2-Fig5.10Fig. 5.10

What this figure shows. Diagram showing the line of slope m crossing the Y-axis at C(0,c), used to derive the slope-intercept form. This figure gives the reader a concrete visual reference for the geometric configuration described in the surrounding text, tying the abstract statement to a pic …

Misc 5.3.2-Ex1Worked example — slope-intercept form

Worked out. Finds the equation of the line with slope 3 and Y-intercept 4 by direct substitution into y = mx + c. Working through this worked example after reading the theory above helps consolidate the method before attempting the exercise questions that follow it in the textbook. …

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