Determine the equation of a line that is perpendicular to the line 5x+y-6=0 and passes through the point (4, -3).

Question

Grade 10 Math

Determine the equation of a line that is perpendicular to the line 5x+y-6=0 and passes through the point (4, -3).

Answer 1

Step 1: Turn the equation into y=mx+b form.

5x+y-6 = 0

+6 +6 Add 6 to both sides

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5x+y = 6

-5x -5x Subtract 5x from both sides

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y = -5x + 6

Step 2: Find the slope of the perpendicular line. Perpendicular lines have slopes that are opposite reciprocal of one another.

The slope of y =-5x + 6 is -5x. The opposite of -5x is 5x and the reciprocal of 5x is 1/5 x.

Equation of the perpendicular line: y = 1/5 x +b

Step 3: Coordinates are written as (x, y) so in the coordinate (4, -3), x is 4 and y is -3. We can replace this in the equation y = 1/5 x +b to solve for b.

y = 1/5 x +b

-3 = 1/5 (4) +b

-3 = 4/5 +b

-4/5 -4/5

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-19/5 = b

Step 4: Write the equation of the perpendicular line in y=mx+b form.

y = 1/5 x - 19/5

Answer 2

Hey there Andrea! Lets start with what this equation is going to look like.

Whatever line we're searching for is going to have a formula like: y=mx+b, and so we just need to solve for m and b.

We know that this new line is going to be perpendicular to the one given to us. Using this, we can figure out m. Recall that if you have slopes m₁ and m₂ then being perpendicular means that m₁*m₂=-1. In this case, the line we started off with is 5x+y-6=0 or when re-written, y=-5x+6. Using this, try to figure out m.

After that, we just need to solve for b. We can do this by plugging in the point (4,-3) into our new line equation, going from y=mx+b to -3=m(4)+b and since we know m, we can solve for it!

Let me know if you still have any questions regarding this. Cheers!