Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).A line passes through point (-2, 5) and has a slope of 2/3 . Points A(x, 3) and B(-2, y) lie on the line.The value of x is__________, and the value of y is __________.

Accepted Solution

Answer: The value of x is -5 and the value of y is 5.Explanation:The slope of the line is [tex]\frac{2}{3}[/tex] and the point is (-2,5) from which the line line is passing.If a line is passing through the point [tex](x_1,y_1)[/tex] with slope m, the the equation of line is,[tex]y-y_1=m(x-x_1)[/tex][tex]y-5=\frac{2}{3}(x+2)[/tex][tex]3y-15=2x+4[/tex][tex]3y-2x=19[/tex] Β  Β ..... (1)It is given that the point A(x,3) and B(-2,y) lies on the line. It means it satisfies the equation of the line.Put y=3 in equation (1).[tex]3(3)-2x=19[/tex][tex]-2x=10[/tex] [tex]x=-5[/tex]The value of x is -5.Put x=-2.[tex]3y-2(-2)=19[/tex][tex]3y+4=19[/tex][tex]3y=15[/tex][tex]y=5[/tex]The value of y is 5.