Question

the slope intercept form of the Equation of a line that passes through the points (-2,-13) is y=5x-3 what is the point slope form of the equation for this line

Answer 1

Well, we know the slope-intercept is y=5x-3 , now   $\bf y=\stackrel{slope}{5}x\stackrel{y-intercept}{-3}$.

reason why is called the slope-intercept form, so, the slope is 5, and we know the line runs through -2,-13, thus

$\bf \begin{array}{ccccccccc} &&x_1&&y_1\\ % (a,b) &&(~ -2 &,& -13~) \end{array} \\\\\\ % slope = m slope = m\implies 5 \\\\\\ % point-slope intercept \stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-(-13)=5[x-(-2)] \\\\\\ y+13=5(x+2)$