Write an equation of the line that passes through (−1,3) and is parallel to the line y=2x+2.

The equation of the line that passes through (−1,3) and is parallel to the line y = 2x + 2 in slope intercept form is y = 2x + 5

Given that line passes through (-1, 3) and parallel to line y = 2x + 2

We have to find the equation of the line

Let us first find the slope of the line

The slope intercept form of line is given as:

y = mx + c   eqn 1

where "m" is the slope of the line and "c" is the y-intercept

Comparing the given line equation y = 2x + 2 with y = mx + c,

We get slope "m" = 2

The slope of parallel lines are equal

Hence slope of the line which is parallel to y = 2x + 2 is also 2

Now let us find the equation of line with slope "m" = 2 and passes through point (-1, 3)

Substitute (x, y) = (-1, 3) in eqn 1 to find value of "c"

3 = 2(-1) + c

3 = -2 + c

c = 5

Now substitute "c" = 5 and m = 2 in eqn 1 to get equation of required line

y = 2x + 5

Thus the equation of line in slope intercept form is y = 2x + 5