This table gives a few (x,y)(x,y)left parenthesis, x, comma, y, right parenthesis pairs of a line in the coordinate plane.xxx yyy−36−36minus, 36 −117−117minus, 117−27−27minus, 27 −98−98minus, 98−18−18minus, 18 −79−79minus, 79What is the yyy-intercept of the line?(

Answer:The y-intercept of the line is the point (0,-41)Step-by-step explanation:we have the points(-36,-117),(-27,-98) and (-18,-79)step 1Find the slope of the linear equationThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] take the points(-27,-98) and (-18,-79)substitute the values[tex]m=\frac{-79+98}{-18+27}[/tex] [tex]m=\frac{19}{9}[/tex] step 2Find the equation of the line in point slope form[tex]y-y1=m(x-x1)[/tex]we have[tex]m=\frac{19}{9}[/tex] [tex]point\ (-18,-79)[/tex]substitute[tex]y+79=\frac{19}{9}(x+18)[/tex] ----> equation in point slope formstep 3Convert the equation in slope intercept form[tex]y=mx+b[/tex]where m is the slopeb is the y-coordinate of the y-interceptisolate the variable y[tex]y+79=\frac{19}{9}x+(18)\frac{19}{9}[/tex][tex]y=\frac{19}{9}x+(18)\frac{19}{9}-79[/tex][tex]y=\frac{19}{9}x+38-79[/tex][tex]y=\frac{19}{9}x-41[/tex]therefore[tex]b=-41[/tex]The y-intercept of the line is the point (0,-41)