How do you find the line through the coordinates (3,-2) and have it be parallel to y=1/2x -2
To find the line through the coordinates (3,-2) and parallel to y = 1/2x - 2, we first need to determine the slope of the given line y = 1/2x - 2.
The slope of a line in the form y = mx + b, where m is the slope, is the coefficient of x (m). So in this case, the slope of the given line y = 1/2x - 2 is m = 1/2.
Since we want the new line to be parallel to the given line, the slope of the new line will also be 1/2.
Now, we can use the point-slope form of the equation of a line to find the equation of the new line passing through the point (3,-2) with a slope of 1/2:
y - y1 = m(x - x1)
where (x1, y1) is the point (3,-2) and m is the slope 1/2.
Plugging in the values, we get:
y - (-2) = 1/2(x - 3)
y + 2 = 1/2x - 3/2
y = 1/2x - 3/2 - 2
y = 1/2x - 3/2 - 4/2
y = 1/2x - 7/2
Therefore, the equation of the line passing through the point (3,-2) and parallel to y = 1/2x - 2 is y = 1/2x - 7/2.