what is the equation of the line through the point (3,3) that is perpendicular to the line y=-1/2x+2

Question

Please help me get my answer right

Answer 1

Linear functions present as: f(x) = mx + b or

y = mx + b. Because the line should be perpendicular to the given line therefore their slope are OPPOSITE. The given line has slope = -1/2 therefore the perpendicular line has slope 2/1 or 2. Because this line pass through point(3,3) therefore we plug in this coordinate and slope in the formula to find b.

3 = 2(3) + b. 3 = 6 + b therefore b = -3.

The equation is: y = 2x -3

Answer 2

Perpendicular lines go in the COMPLETELY opposite directions. If one line is increasing (goes up) the perpendicular line is decreasing (goes down). If one is steep, the perpendicular line is shallow. Visualize this. This will help you remember the perpendicular line has a slope of the negative AND reciprocal (flip the fraction upside down) of the original slope.

Your line has slope - 1/2. The perpendicular line has slope + 2/1, or 2.

So the answer will have the equation y = 2x +b. What's b, the y intercept? Well you know if a point is on the line, it MUST work in the equation of the line. SO you can plug in the given point, (3,3), that is: use x=3 and y=3, and solve for b.

OR - you can use POINT-SLOPE form of a line, (y - y₁) = m (x - x₁) using m = 2 and (x₁, y₁) = (3,3) Either way, you will get the equation of the line perpendicular to your given line and goes through (3,3).

Good luck!