Question

all lines whose slopes and x intecept equal Ans. y=y'x-y'^2

Answer 1

help

Answer 2

what you have tried ?

Answer 3

\[y=mx+b\]

Answer 4

y=bx+b
y'=b

Answer 5

subst. y=y'x+y'
factor out

Answer 6

y=y'(x+1)

Answer 7

what is the next step ? @amoodarya

Answer 8

Looks you're wrongly assuming \(b\) is the x intercept

Answer 9

For a straight line, \(y = mx + b\), the x intercept can be worked by plugging in \(y=0\) :
\[0 = mx+b \implies x = -\frac{b}{m}\]

Answer 10

therefore \(-\frac{b}{m}\) is the x intercept, not \(b\)

Answer 11

Since you want that equal to the slope, \(-\frac{b}{m}=m \implies b=-m^2\) and the equation of line becomes :
\[y = mx-m^2\]

plugin \(m=y'\) and you're done!

Answer 12

@ganeshie8 thank you , i did it :)

Answer 13

@ganeshie8 same answer :)