Question 1133321
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There are an infinite number of parameterized forms of the equation....<br>
The slope-intercept form of the equation through the two given points is<br>
{{{y = (4/3)x-26/3}}}<br>
An equivalent equation is then<br>
{{{3y = 4x-26}}}<br>
or<br>
{{{4x-3y = 26}}}<br>
From this form, we can see that any parameterized form has to be of the form<br>
{{{y = 4t+a}}}
{{{x = 3t+b}}}<br>
If we let t=0 correspond to the point (5,-2), then the parameterized equations are<br>
{{{y = 4t-2}}}
{{{x = 3t+5}}}<br>
If we let t=0 correspond to the point (8,2), then the parameterized equations are<br>
{{{y = 4t+2}}}
{{{x = 3t+8}}}<br>
And of course we can get other parameterized equations by letting t=0 correspond to some other point on the line through the two given points.