the straight line l1 has equation y=2x+3
the straight line l2 is parallel to l1
l2 passes through the point (3,2)
find an equation for l2
The slope is m = 2.
For L2, the formula is
(y - 2)/(x - 3) = 2
Rearrange that to the standard form
To find an equation for the line l2, which is parallel to l1 and passes through the point (3,2), we can use the fact that parallel lines have the same slope.
Since the equation of l1 is y = 2x + 3, we can see that the slope of l1 is 2. Therefore, the slope of l2 will also be 2.
Using the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line, we can substitute the values for m, x1, and y1.
Let's substitute m = 2, x1 = 3, and y1 = 2 into the equation:
y - 2 = 2(x - 3)
Now, let's simplify the equation:
y - 2 = 2x - 6
Next, let's bring the constant term to the other side:
y = 2x - 6 + 2
Simplifying further:
y = 2x - 4
Therefore, the equation for l2, the line parallel to l1 and passing through the point (3,2), is y = 2x - 4.
To find the equation for line l2, which is parallel to line l1 and passes through the point (3, 2), you can use the fact that parallel lines have the same slope.
Since line l1 has the equation y = 2x + 3, we can see that its slope is 2. Any line parallel to it will also have a slope of 2.
Using the point-slope form of a linear equation, we can plug in the slope of 2 and the given point (3, 2) to find the equation for line l2.
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
Where:
m is the slope of the line
(x1, y1) is a point on the line
In this case, the slope m = 2 and the point (x1, y1) = (3, 2).
Plugging these values into the equation, we get:
y - 2 = 2(x - 3)
Now, you can simplify the equation to find an equation for l2:
y - 2 = 2x - 6
Add 2 to both sides:
y = 2x - 4
Therefore, the equation for line l2 is y = 2x - 4.