Answer:
Point-Slope Form: y - 1 = -1/2(x - 4) or Standard Form: y = -1/2x + 3
Step-by-step explanation:
For a line to be perpendicular, you take the negative inverse of the slope of 2x - y = 4. To do this, rearrange the y to one side and you get y = 2x - 4. The slope of the line is 2. So, taking the negative inverse would be -1/m (with m being slope of the the equation given in the problem. This would give you -1/2.
Using point slope formula, y - y1 = m(x - x1), you can plug in the point given, (4,1) and the slope you found to get y - 1 = -1/2(x - 4). For standard form, isolating the y gets you y = -1/2x + 3.
You can check your answer by using Desmos by putting in the line 2x - y = 4, the point (4,1), and the equation you got as your answer. You will see that the equation is perpendicular to 2x - y = 4 and passes through point (4,1). Your equation of the line is y - 1 = -1/2(x - 4) or y = -1/2x + 3
Hope this helps!
Here, we are required to find the equation of the line that passes through the point (4,1) and is
perpendicular to the line 2x - y = 4.
The equation of the line is: y = (-x/2) + 3
First, the product of the slopes of 2 perpendicular lines is -1.
Therefore, M1 × M2 = -1.
By rearranging the equation 2x - y = 4 to mimic the equation of a straight line; y = mx + c.
we have, y = 2x + 4 and obviously slope, m1 = 2.
Therefore, since M2 = -1/M1 from above;
M2 = -1/2
Therefore, the equation of the required line is given by;
M2 = (y - y1)/(x - x1)
where, M2 = -1/2, y1 = 1 and x1 = 4.
Ultimately, -1/2 = (y - 1)/(x - 4)
The equation of the line is then given as;
y = (-x/2) + 3.
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