Mathematics

Problem

In the equation

y - y_1 = m(x - x_1)

of a straight line, write an expression for the

y

-intercept when the same line is expressed in the form

y = mx + c

Intuitive explanation

The key insight is that both forms describe the same line, so you can convert between them algebraically. Start with point-slope form $y - y_1 = m(x - x_1)$ , expand it, and rearrange to isolate $y$ on one side—this reveals $c$ as the constant term that emerges. The $y$ -intercept is simply what you get when you solve for the constant in slope-intercept form.

Intuitive explanation

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