Question

A line runs through (-5, -4) and has a slope of 17/7 what is the y intercept

Answer 1

(0, 57/7)

Explanation:

Start with y = mx + b. Substitute -5 for x, -4 for y and 17/7 for m, and then find b:

-4 = (17/7)(-5) + b

Multiply all terms by 7 to eliminate the fractions:

-28 = 17(-5) + 7b, or -28 + 85 = 7b. Then 7b = 57, and b = 57/7.

The y-intercept is (0, 57/7).

Answer 2

`\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-4})~\hspace{10em}slope = m\implies \cfrac{17}{4}\\\\\\ \begin{array}c\cline{1-1}\textit{point-slope form}\\\cline{1-1}\\y-y_1=m(x-x_1)\\\\\cline{1-1}\end{array}\implies y-(-4)=\cfrac{17}{7}[x-(-5)]\implies y+4=\cfrac{17}{7}(x+5)\\\\\\y+4=\cfrac{17}{7}x+\cfrac{85}{7}\implies y=\cfrac{17}{7}x+\cfrac{85}{7}-4\implies y=\cfrac{17}{7}x+\cfrac{57}{7}`

`\bf y=\cfrac{17}{7}x+8(1)/(7)\leftarrow \begin{array}\cline{1-1}slope-intercept~form\\\cline{1-1}\\y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}}\\\\\cline{1-1}\end{array}\implies \blacktriangleright \stackrel{y-intercept}{\left( 0, 8(1)/(7) \right)} \blacktriangleleft`