A few days ago
Mr T

# math question?

If y = ax + b is the equation of the line that passes through (2, 4) and is perpendicular to the line y = 5x + 1, find a and b.

A few days ago
Twinky

see y=ax+b

(2,4)…are cordinates (x,y)

so put x=2 and y=4

now u have

4=2a+b—-> equation 1

if y=5x+1 and y=ax+b [or 4=2a+b] are perpendicular then

gradient of y=5x+1 is 5 bcz y=mx+c

gradient of first eq. is a

since every line has eq. y=mx+c

and in this case line is y=ax+b

so….we have

5xa=-1

so a is -1/5

now lets find b

in eq 1. put value of a

4=2a+b

4=-2/5 +b

4+ 2/5=b

b=22/5

b=4 2/5

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A few days ago
math guy
Twinky is correct, but let me try to be shorter and clearer.

Since the slope of y = 5x + 1 is 5, the slope of y = ax + b will be -1/5.

Using point-slope form: y – y1 = m(x – x1), we get

y – 4 = -1/5(x – 2)

y = -1/5 * x + 4 + 2/5

y = -0.2x + 4.4

a = -0.2 = -1/5

b = 4.4 = 4 and 2/5 = 22/5

I hope this helps!

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A few days ago
Anonymous
perpendicular means the slope is a reciprocal, which in this case is 1/5.

thus: y=1/5x+b

since the line passes through (2,4), plug those in to the equation for x and y,

4=1/5(2)+b

b=4-1/5(2)

b=3.6

a=0.2

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A few days ago
Twiggy
Its gradient will be -1/5, not 1/5,
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