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Exercises for HELM Book 2.5.3.

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Find the equation of a line through 2 points. The line is not vertical.

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Calculate the equation of the line joining $(\\var{x1},\\var{y1})$ and $(\\var{x2},\\var{y2})$

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\\[ \\begin{align*} \\frac{y-y_1}{x-x_1} &= \\frac{y_2-y_1}{x_2-x_1}\\\\ \\frac{y-(\\var{y1})}{x-(\\var{x1})}&=\\frac{\\var{y2}-(\\var{y1}) }{\\var{x2}-(\\var{x1})} \\\\ \\frac{\\var{yminusy1e}}{\\var{xminusx1e}} &=\\var{expression(string(rational((y2-y1)/(x2-x1))))}\\\\ \\var{yminusy1e}&=\\var{expression(string(rational((y2-y1)/(x2-x1))))}(\\var{xminusx1e})\\\\ \\textrm{So }\\qquad y&=\\var{expression(string(rational((y2-y1)/(x2-x1))))}(\\var{xminusx1e}) +\\var{y1}\\\\&=\\var{eqn} \\end{align*}\\]

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$y=$[[0]]

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Find the gradient and y-axis intercept of a line through 2 points. The line is not vertical.

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Calculate the gradient and vertical intercept of the line joining $(\\var{x1},\\var{y1})$ and $(\\var{x2},\\var{y2})$

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Thus, gradient = $\\displaystyle{\\var{me}}$, and vertical intercept = $\\displaystyle{\\var{be}}$

gradient = [[0]]

vertical intercept = [[1]]

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This quiz is a Numbas implementation of the Helping Engineers Learn Maths (HELM) booklet 2.5, The straight line.

Questions generally have multiple versions, clicking the \"Try another question like this one\" button will generate a new version.

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