Find the equation of the line passing through (-1,2) and parallel to y=2x-1.
I don't understand how to figure out this problem.
Thank you! :-)
To find the equation of a line that is parallel to another line, you need to use the fact that parallel lines have the same slope.
In the given equation, y = 2x - 1, the slope is 2 (the coefficient of x). Therefore, any line that is parallel to this line will also have a slope of 2.
Now, to find the equation of the line passing through the point (-1,2) with a slope of 2, we can use the point-slope form of the equation of a line:
y - y1 = m(x - x1)
In this equation, (x1, y1) represents the coordinates of the given point, and m represents the slope of the line.
Substituting the values of the given point (-1,2) and the slope 2 into the point-slope form, we have:
y - 2 = 2(x - (-1))
Simplifying, we get:
y - 2 = 2(x + 1)
Expanding the right side:
y - 2 = 2x + 2
To isolate y, we can add 2 to both sides:
y = 2x + 4
Therefore, the equation of the line passing through (-1,2) and parallel to y = 2x - 1 is y = 2x + 4.