Question

if a line contains the point (0,-1) and has a slope of 2, then what point lies on the line?

Answer 1

we first determine the equation of the line using the slope-intercept form

y = mx + b

where m = slope
b = y-intercept

given a slope of 2, the equation of the line would initially look like this:

y = 2 x + b

to compute for b, we substitute the values of point ( 0, -1 ) to the equation

-1 = ( 2 ) ( 0 ) + b
-1 = 0 + b
-1 = b
b = -1

the equation of the line is therefore

y = 2 x - 1

to determine which of the following points also lies on the line, simply substitute the value of x and see if the resulting y is the same as the y of the point in question.

a) ( 2, 1 )
y = ( 2 ) ( 2 ) - 1 = 4 - 1 = 3
does not lie on the line

b) ( 1, 1 )
y = ( 2 ) ( 1 ) - 1 = 2 - 1 = 1
this point lies on the line

c) ( 0, 1 )
y = ( 2 ) ( 0 ) - 1 = 0 - 1 = -1
does not lie on the line