Find the equation of a line which passes through point P(10, 12) and // to y=x/2 + 4
since it is parallel to y=x/2 + 4
it will differ only in the y-intercept, so let
y=x/2 + b
plug in the point(10,12)
12 = 5+b
b = 7
y = x/2 + 7
or, you can avoid b altogether and go straight to the point-slope form of the line with slope 1/2:
y-12 = 1/2 (x-10)
To find the equation of a line parallel to another line, we need to determine the slope of the given line and then use the given point to find the equation.
The given line is parallel to the line with the equation y = (1/2)x + 4. The slope of this line is 1/2.
The equation of a line in slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.
Since the line we want is parallel to the given line, it would have the same slope of 1/2. Let's use the point-slope form of a line to find the equation.
The point-slope form is given by y - y₁ = m(x - x₁), where (x₁, y₁) is the given point and m is the slope.
Using the point P(10, 12) and m = 1/2, we substitute the values into the equation:
y - 12 = (1/2)(x - 10)
Next, simplify the equation:
y - 12 = (1/2)x - 5
To get the equation in slope-intercept form, isolate y:
y = (1/2)x - 5 + 12
y = (1/2)x + 7
Therefore, the equation of the line that passes through the point P(10, 12) and is parallel to y = (1/2)x + 4 is y = (1/2)x + 7.