On Point Forms and Slope Formulae

In the realm of lines, with slopes and points,

Two forms of equations, each anoints.

Point-slope and slope-intercept, distinct they stand,

Let’s explore their differences, hand in hand.

First, the point-slope form, a guiding light,

For lines through a point, it’s just right.

$y - y_1 = m(x - x_1)$

It starts with a point, and a slope to align.

$(x_1, y_1)$ is where it begins,

With slope $m$ , the line’s path it spins.

A flexible form, for points well known,

From any position, the line is shown.

Next, the slope-intercept, so sleek and clear,

$y = mx + b$ , it brings cheer.

Where $m$ is the slope, rise over run,

And $b$ is the intercept, where it’s begun.

On the y-axis, the line will start,

With $b$ as its mark, a crucial part.

From there, the slope guides its rise,

A straight path drawn before our eyes.

Point-slope for specifics, a point and a slope,

A form that gives lines a flexible scope.

Slope-intercept for clarity, with $b$ and $m$ ,

A straightforward path, a linear gem.

Two forms of lines, each with its place,

In the world of math, they find their grace.

Point-slope for precision, slope-intercept for ease,

Both guide our lines with mathematical keys.

Published by Clark Vangilder