write an equation of the line that is parallel to the given line and passes through the given point
A. y=5x-2 passing through (2,-1)
b. y=9x passing through (0, -5)
A. To find the equation of a line that is parallel to y=5x-2 and passes through (2,-1), we know that parallel lines have the same slope. Therefore, the slope of the new line will also be 5.
Using the point-slope form of a linear equation, the equation of the line is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Plugging in the values, we have:
y - (-1) = 5(x - 2)
y + 1 = 5x - 10
Simplifying the equation, we get:
y = 5x - 11
Therefore, the equation of the line parallel to y=5x-2 passing through (2,-1) is y = 5x - 11.
B. To find the equation of a line that is parallel to y=9x and passes through (0, -5), we again know that parallel lines have the same slope. Therefore, the slope of the new line will also be 9.
Using the point-slope form of a linear equation, the equation of the line is:
y - y1 = m(x - x1)
where m is the slope and (x1, y1) is the given point.
Plugging in the values, we have:
y - (-5) = 9(x - 0)
y + 5 = 9x
Simplifying the equation, we get:
y = 9x - 5
Therefore, the equation of the line parallel to y=9x passing through (0, -5) is y = 9x - 5.