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 parallel to a given line, we need to remember that parallel lines have the same slope. The given line has a slope of 2 because it's in the form of y = mx + b, where m represents the slope.
We can directly use the point-slope form of a linear equation to find the equation of the line passing through (-1,2) and having a slope of 2.
The point-slope form of a linear equation is: y - y1 = m(x - x1)
Here, (x1, y1) represents the coordinates of the given point (-1,2), and m is the slope we already know to be 2.
Substituting these values into the equation, we get:
y - 2 = 2(x - (-1))
Simplifying further, we have:
y - 2 = 2(x + 1)
Expanding the parentheses, we get:
y - 2 = 2x + 2
Finally, to write the equation in standard form, we bring all the terms to one side of the equation:
2x - y = -4
Therefore, the equation of the line passing through (-1,2) and parallel to y = 2x - 1 is 2x - y = -4.