Short answer

a) write the equation in standard form for the line that passes through the points ( - 5, 1 ) and ( 6, -2 ). b) write the equation in standard form for the line that passes through the points ( 4, -2 ) and ( 4, 8 ).

(-5,1)(6,-2)
slope = (-2-1) / (6-(-5) = -3/(6 + 5) = -3/11

y = mx + b
slope(m) = -3/11
(-5,1)...x = -5 and y = 1
now we sub and find b, the y int
1 = -3/11(-5) + b
1 = 15/11 + b
1 - 15/11 = b
11/11 - 15/11 = b
-4/11 = b
equation in slope int form : y = -3/11x - 4/11
3/11x + y = - 4/11multiply by 11
3x + 11y = -4 <== standard form

(4,-2)(4,8)if u will notice, both the x values are the same. This means the lines are vertical with an undefined slope. Your equation is : x = 4.