X+4y=4 in slope intercept form
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First off, let's solve <span>x−5y=15 for "y".
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now, notice the function in slope-intercept form, well, it has a slope of 1/5.
now, a perpendicular line to that one, will have a negative reciprocal to that, let's check what that is.
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so, we're looking for the equation of a line whose slope is -5 and goes through -2,5.
</span>![\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -2}}\quad ,&{{ 5}}) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies -5 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-5=-5[x-(-2)] \\\\\\ y-5=-5(x+2)\implies y-5=-5x-10\implies y=-5x-5](https://tex.z-dn.net/?f=%5Cbf%20%5Cbegin%7Barray%7D%7Blllll%7D%0A%26x_1%26y_1%5C%5C%0A%25%20%20%20%28a%2Cb%29%0A%26%28%7B%7B%20-2%7D%7D%5Cquad%20%2C%26%7B%7B%205%7D%7D%29%0A%5Cend%7Barray%7D%0A%5C%5C%5C%5C%5C%5C%0A%25%20slope%20%20%3D%20m%0Aslope%20%3D%20%7B%7B%20m%7D%7D%3D%20%5Ccfrac%7Brise%7D%7Brun%7D%20%5Cimplies%20-5%0A%5C%5C%5C%5C%5C%5C%0A%25%20point-slope%20intercept%0A%5Cstackrel%7B%5Ctextit%7Bpoint-slope%20form%7D%7D%7By-%7B%7B%20y_1%7D%7D%3D%7B%7B%20m%7D%7D%28x-%7B%7B%20x_1%7D%7D%29%7D%5Cimplies%20y-5%3D-5%5Bx-%28-2%29%5D%0A%5C%5C%5C%5C%5C%5C%0Ay-5%3D-5%28x%2B2%29%5Cimplies%20y-5%3D-5x-10%5Cimplies%20y%3D-5x-5)
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</span>
<span>
now, notice the function in slope-intercept form, well, it has a slope of 1/5.
now, a perpendicular line to that one, will have a negative reciprocal to that, let's check what that is.
</span>
<span>
so, we're looking for the equation of a line whose slope is -5 and goes through -2,5.
</span>
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