Answer:
The equation of a line through (5 -3) that is parallel to y = 1/2 x+3 is
y = - 2 x + 7
Explanation:
Let us assume the slope of the line whose equation we need to find is m 1.
The line parallel to the needed line is: y=1/2x+3
Comparing it with the general form: y = m x + C
we get m 2 = 1/2
Now, as Line 1 is Perpendicular to Line 2.
⇒ m 1 x m 2 = -1
⇒ m 1 x ( 1/2) = -1
⇒ m 1 = - 2
Also, the point son the line 1 is given as: (x,y) = (5,-3)
Put the value of point and Slope in y = m x + C to find the value of Y- INTERCEPT.
we get: -3 = (-2) (5) + C
or, C = -3 + 10 = 7
⇒ C = 7
The general line equation is given as: y = m x + C
Substituting the values of C and m, we get:
y = - 2 x + 7
Hence, the equation of a line through 5 -3 that is parallel to y = 1/2 x+3 is
y = - 2 x + 7