Sara walks 2 m every second → y = 2x
Sara walks two meters every second. Let's graph her distance over time and find the equation for her line.
First, we draw axes: time on the x-axis, distance on the y-axis.
After one second, she's walked two meters. Plot the point one, two.
After two seconds, she's walked four meters. Plot two, four.
These points sit on a straight line that passes right through the origin.
From the origin to the first point, we go right one and up two. That's a small right triangle.
From the origin to the second point, we go right two and up four. A bigger triangle, but the same shape.
Both triangles are similar — their rise over run is the same. Two over one equals four over two equals two.
That common ratio is the slope. We call it m. Here, m equals two.
For every point on the line, y over x equals m. Multiply both sides by x and we get y equals m times x.
Sara's line is y equals two x. Every line through the origin follows y equals m x, where m is its slope.