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
<h3><u>Solution</u>:</h3>
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
<em><u>The slope intercept form of line is given as:</u></em>
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
