Question

Write an equation of the line that passes through point (4,12) and has a y intercept of -2

Answer 1

now let's plug those coordinate values in the point-slope form, with say a slope of "m",


`\bf (4~,~12)\qquad \qquad \stackrel{\textit{point-slope form}}{y-{{ y_1}}={{ m}}(x-{{ x_1}})}\implies y-12=m(x-4) \\\\\\ y-12=mx-4m\implies y=\stackrel{slope}{m}x~\stackrel{y-intercept}{-4m+12}`

we know the y-intercept in that slope-intercept form, has to be "-2", so whatever "-4m+12" is, must be -2, thus,


`\bf -4m+12=-2\implies 14=4m\implies \cfrac{14}{4}=m\implies \boxed{\cfrac{7}{2}=m}\\\\ -------------------------------\\\\ y=\cfrac{7}{2}m-4\left( \cfrac{7}{2} \right)+12\implies y=\cfrac{7}{2}m-14+12 \\\\\\ y=\cfrac{7}{2}m-2`