Graph linear and quadratic functions and show key features such as intercepts, maxima, and minima.
Graph a line through two points
Problem
Graph the line through \((1,~2)\) and \((4,~8)\), and give its equation.
The two points determine a line with slope 2.Open full size
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What this problem is really about
Two distinct points determine exactly one line. We’ll plot both coordinates, compute vertical change over horizontal change in a consistent direction, and use one point with that slope to recover the intercept. Checking both given points in the resulting equation identifies the matching graph and confirms that rise and run were not accidentally reversed.
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