Question

test yourself! practice tool
all three points displayed are on the line below. which equation relates x to y?
(3, 4), (9, 12), (x, y) are on the line.

Explanation:

Step1: Calculate the slope

The slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m = \frac{y_2 - y_1}{x_2 - x_1} \). Using the points \((3, 4)\) and \((9, 12)\), we have \( m = \frac{12 - 4}{9 - 3} = \frac{8}{6} = \frac{4}{3} \).

Step2: Use point - slope form

The point - slope form of a line is \( y - y_1 = m(x - x_1) \). Using the point \((3, 4)\) and \( m=\frac{4}{3} \), we get \( y - 4=\frac{4}{3}(x - 3) \).

Step3: Simplify the equation

Expand the right - hand side: \( y - 4=\frac{4}{3}x-4 \). Then add 4 to both sides: \( y=\frac{4}{3}x \), or cross - multiplying gives \( 3y = 4x \) or \( y=\frac{4}{3}x \).

Answer:

The equation relating \( x \) and \( y \) is \( y=\frac{4}{3}x \) (or equivalent forms like \( 4x - 3y = 0 \))