Write the equation of the line satisfying the given condition.
Parallel to y = (2/3)x +1 and passing through the point (0, -3).
(Hint: Parallel lines have the same slope
since (0,-3) is the y-intercept, without any work we can write the answer as
y = (2/3)x - 3
To find the equation of a line parallel to a given line, you need to determine its slope. The given line is y = (2/3)x + 1. Since the equation is in slope-intercept form (y = mx + b), the slope of the line is the coefficient of x, which in this case is 2/3.
Since parallel lines have the same slope, the slope of the line we are looking for is also 2/3.
Now that we have the slope of the line and a point it passes through (0, -3), we can use the point-slope form of a linear equation to find the equation of the line.
The point-slope form of a linear equation is given by y - y₁ = m(x - x₁), where (x₁, y₁) is the point and m is the slope.
Plugging in the values, we have:
y - (-3) = (2/3)(x - 0)
Simplifying this equation, we get:
y + 3 = (2/3)x
To make it in the slope-intercept form, we can move the 3 to the other side:
y = (2/3)x - 3
Therefore, the equation of the line parallel to y = (2/3)x + 1 and passing through the point (0, -3) is y = (2/3)x - 3.