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I would like to find a point $d$ away on a line from a starting point only given a slope. My fist thought was to use the distance formula ($d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$), but I would have to solve for two variables. How can I solve find the point without graphing or brute forcing?

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If $m$ is the given slope, you also have $y_2-y_1=m(x_2-x_1)$, so $$d=\sqrt{1+m^2}|x_2-x_1|\\x_2=x_1\pm \frac d{\sqrt{1+m^2}}$$

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