Question

3a. Write an equation in slope-intercept form of a
line that passes through (2,1) and (6,-5).

Answer 1

`y = -3/2x + 4`

Explanation:

`(2,1) and (6,-5).\\x_1 = 2\\x_2 = 6\\y_1 =1\\y_2 =-5\\(y-y_1)/(x-x_1) = (y_2-y_1)/(x_2-x_1)\\ \\(y-1)/(x-2) = (-5-1)/(6-2)\\\\(y-1)/(x-2) = (-6)/(4) \\Cross-Multiply\\4(y-1) = -6(x-2)\\4y-4=-6x+12\\4y =-6x+12+4\\4y = -6x+16\\Divide through-by ; 4\\(4y = -6x+16)/(4) \\\\y = -(3)/(2) x +4`