Question

What is the point slope equation of line that passes through the point (5,2) and has the same y intercept as y=3x-9

Answer 1

so we know it passes through 5,2, and has the same y-intercept as y = 3x -9.... hmmmm
`\bf y=\stackrel{slope}{3}x\stackrel{y-intercept}{-9}`.

so this one has a y-intercept at -9, therefore this line must have the same y-intercept... let's say it has a slope of "m".




so, this one has a y-intercept of "-5m+2", which we know is the same as the other equation's, therefore -5m+2 = -9.


`\bf -5m+2 = -9\implies -5m=-11\implies m=\cfrac{-11}{-5}\implies m=\cfrac{11}{5}\\\\ -------------------------------\\\\ \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-2=m(x-5)\implies y-2=\cfrac{11}{5}(x-5)`