Question

The line is parallel to y= 2x + 1 and passes through point (-2,-1).

Answer 1

y = 2x + 3

Explanation:

To find the equation of a line, you need 2 things:

1) gradient/slope

2) 1 set of x and y coordinates

To find the slope:

If 2 lines are parallel, they have exactly the same gradient.

So, this line will have a slope of 2 as well (the slope of a line is the coefficient of x in the equation).

To find the equation of the line:

Start with this generic equation:

y - y1 = m (x-x1)

We know that:

(x1, y1) -> (-2, -1) and m= 2

So, we can substitute for the equation:

y- (-1) = 2 (x -(-2))

Simplify, by expanding the brackets:

y + 1= 2 (x+2)

y + 1 = 2x + 4

Rearrange for y:

y = 2x + 3

To double check:

1) The coefficient of x is the slope, we have 2x and the slop is 2, so that's correct

2) Sub in x= -2, and you should get y=-1

y = -4 + 3 = -1, so that's correct too

Hope that helped : )