Line Through Two Points

Given $(x_1, y_1)$ and $(x_2, y_2)$, the slope is $m = \frac{y_2 - y_1}{x_2 - x_1}$ and the equation is $y - y_1 = m(x - x_1)$. So for $(1, 2)$ and $(3, 6)$, $m = 2$ and the line is $y = 2x$. This two-point form is unavoidable in coordinate geometry.

Slide the four coordinates $x_1, y_1, x_2, y_2$. The lab computes slope $m$, y-intercept $c$ and writes the equation $y = mx + c$. Test edge cases like $x_1 = x_2$ (vertical line, undefined slope) to see how the lab handles division by zero.

The slope $m = (y_2 - y_1)/(x_2 - x_1)$ has zero in the denominator. The line is vertical, equation $x = x_1$, and slope is undefined. Many students write $m = \infty$ — formally wrong. Board examiners deduct marks; the lab shows NaN so you learn to spot the case.

Plotting a child's growth chart from height at age 5 and age 10 gives a line; the slope is the growth rate per year. Trend lines on a Sensex chart, dose-response in pharmacology, and depreciation of a Maruti Swift over years all use the same two-point recipe.