Question

name: date: ny - s.ee.6 use similar triangles to explain why the slope m is the same between any two distinct points on a non - vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b. mathematical practices: mp3, mp6, mp7 example 1: finding the slope of a line: slope $(m)=\frac{\text { height }}{\text { base }}$ slope $m=$ y intercept $=(quad, quad)$ equation $y=m x+b=$ slope $(m)=\frac{\text { height }}{\text { base }}$

Explanation:

Step1: Calculate the slope

Using the formula \(m=\frac{y_1 - y_2}{x_1 - x_2}\), with \((x_1,y_1)=(3,6)\) and \((x_2,y_2)=(-1,-6)\).
\(m=\frac{6-(-6)}{3-(-1)}=\frac{6 + 6}{3+1}=\frac{12}{4}=3\)

Step2: Find the \(y\) - intercept

The \(y\) - intercept is the point where \(x = 0\). From the graph, when \(x = 0\), \(y=-3\), so the \(y\) - intercept is \((0,-3)\)

Step3: Write the equation

Using \(y=mx + b\), where \(m = 3\) and \(b=-3\)
\(y=3x-3\)

Answer:

Slope \(m = 3\); \(Y\) intercept \(=(0,-3)\); Equation \(y=3x - 3\)