Write an equation of the line that is parallel t the given line and passes through the given point.
1. y=3x-8;(0,2)
2. y=-x; (0,6)
1. slope = 3
y = 3 x + b
so to find b
2 = 0 + b
b = 2
y = 3 x + 2
2. same way but slope = -1
To find the equation of a line that is parallel to a given line and passes through a given point, you will need to use the point-slope form of a linear equation.
1. Given line: y = 3x - 8; Point: (0,2)
Since the given line has a slope of 3, the parallel line will also have a slope of 3. Using the point-slope form, the equation can be written as:
y - y1 = m(x - x1)
Here, m is the slope and (x1, y1) is the given point.
Plugging in the values, we have:
y - 2 = 3(x - 0)
Simplifying the equation further:
y - 2 = 3x
The final equation of the line that is parallel to y = 3x - 8 and passing through the point (0,2) is y = 3x - 2.
2. Given line: y = -x; Point: (0,6)
Since the given line has a slope of -1, the parallel line will also have a slope of -1. Using the point-slope form, the equation can be written as:
y - y1 = m(x - x1)
Plugging in the values:
y - 6 = -1(x - 0)
Simplifying the equation:
y - 6 = -x
The final equation of the line that is parallel to y = -x and passing through the point (0,6) is y = -x + 6.