Find the equation of the line which passes through (-4, 3) and parallel to line y = 2x + 5.
Answer Details
To find the equation of a line that is parallel to a given line, we need to use the fact that parallel lines have the same slope.
The given line has a slope of 2 (since it is in the form y = mx + b, where m is the slope and b is the y-intercept). Therefore, any line parallel to it must also have a slope of 2.
We also know that the line passes through the point (-4, 3). We can use the point-slope form of the equation of a line to find the equation of the line:
y - y1 = m(x - x1)
where (x1, y1) is the point the line passes through, and m is the slope.
Substituting in the values we know, we get:
y - 3 = 2(x - (-4))
Simplifying:
y - 3 = 2(x + 4)
y - 3 = 2x + 8
y = 2x + 11
Therefore, the equation of the line which passes through (-4, 3) and parallel to line y = 2x + 5 is y = 2x + 11.
So the answer is: y = 2x + 11.