Solution: The slope $ m $ of the line is $ \frac{19 - 7}{9 - 3} = \frac{12}{6} = 2 $. Using point-slope form with point $ (3, 7) $: $ y - 7 = 2(x - 3) $. Simplify: $ y = 2x - 6 + 7 = 2x + 1 $. The $ y $-intercept occurs when $ x = 0 $, so $ y = 2(0) + 1 = 1 $. Thus, the $ y $-intercept is $ \boxed{1} $.

Sun, 03 May 2026 16:06:20 +0000

How to Find the Equation of a Line Using Point-Slope Form: A Step-by-Step Guide Learning how to determine the equation of a line is a fundamental skill in algebra, essential for graphing and analyzing linear relationships. One powerful method is using the point-slope form, which makes it simple to construct a line when you know a point it passes through and its slope. In this article, we’ll explore how to derive the equation of a line step-by-step, using a real-world example to illustrate the entire process—and how to identify the $ y $-intercept accurately. ### Step 1: Understand the Point-Slope Form The point-slope form of a line’s equation is written as:
$$
y - y_1 = m(x - x_1)
$$
where:
- $ m $ is the slope of the line
- $ (x_1, y_1) $ is any known point on the line
- $ (x, y) $ are the coordinates of any other point on the line