Finding the Equation of a Perpendicular Line Passing Through Two Points

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In summary, the problem involves finding an equation for a straight line passing through points A(3,4) and B(7,-6) that is perpendicular to AB. The first step is to calculate the gradient of AB by using the formula (y2-y1)/(x2-x1). The conversation then discusses the relationship between the slopes of perpendicular lines, which is that they are negative reciprocals of each other. This leads to the conclusion that the gradient of the desired line is 2.5.
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ruby_duby
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equation of a line problem!

The points A and B have co-ordinates (3,4) and (7,-6) respectively. the straight line S passes through A and is perpendicular to AB.
FInd an equation for S, giving your answer in the form ax+by+c=0

Ok so I am really stuck on this question. So far i have calculated the gradient of the line AB by doing (-6-4)/(7-3) and i got -2.5

But now i don't know what to do please help :rolleyes:
 
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  • #2
How are the slopes of perpendicular lines related?
 
  • #3
i have no idea how the slopes are related
 
  • #4
Two lines with gradients m and m' are perpendicular if (m)(m')=-1
 
  • #5
so would that mean that my gradient is +2.5
 
  • #6
Would it?

If m' x (-2.5) = -1, what does m' = ?
 

1. What is the equation of a line?

The equation of a line is a mathematical representation of a straight line on a graph. It is typically written in the form y=mx+b, where m is the slope of the line and b is the y-intercept.

2. How do you find the equation of a line given two points?

To find the equation of a line given two points, first calculate the slope using the formula (y2-y1)/(x2-x1), where (x1,y1) and (x2,y2) are the coordinates of the two points. Then, substitute the slope and one of the points into the equation y=mx+b and solve for b. The resulting equation will be the equation of the line.

3. What is the point-slope form of a line?

The point-slope form of a line is another way to write the equation of a line. It is written in the form y-y1=m(x-x1), where (x1,y1) is a point on the line and m is the slope. This form is useful when you know the slope and one point on the line.

4. How do you convert the equation of a line from point-slope form to slope-intercept form?

To convert the equation of a line from point-slope form to slope-intercept form, you can use algebraic manipulation. First, distribute the slope to the terms inside the parentheses. Then, solve for y to isolate it on one side of the equation. The resulting equation will be in the form y=mx+b, where m is the slope and b is the y-intercept.

5. Can the equation of a line have a negative slope?

Yes, the equation of a line can have a negative slope. This means that the line is decreasing as you move from left to right on the graph. The slope is a measure of how steep the line is, and a negative slope indicates that the line is sloping downwards.

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