Question

The equation of the straight line whose inclination is π/4
and x-intercept is 4 is ax + by + c = 0 then a + b + c =
4​

Answer 1

The equation of the straight line whose inclination is π/4 and x - intercept is 4 is ax + by + c = 0

To find : the value of (a + b + c)

solution : The equation of the straight line whose inclination is π/4.

so, slope of line = tan(π/4) = 1

but we know, slope of line = - coefficient of x/coefficient of y

⇒1 = - a/b .......(1)

as x - intercept of (ax + by + c) = 0, is -c/a

and y intercept of (ax + by + c) = 0, is -c/b

so, x - intercept/y - intercept = b/a ....(2)

from equations (1) and (2) we get,

1 = - y - intercept/x - intercept

⇒1 = -y - intercept/4

⇒y - intercept = -4

then equation of line, x/a + y/b = 1

⇒x/4 + y/-4 = 1

⇒x - y = 4

⇒(1)x + (-1)y + (-4) = 0 on comparing to (ax + by + c) = 0, we get,

a = 1, b = -1 and c = -4

so, a + b + c = 1 - 1 - 4 = -4

Therefore the value of (a + b + c) = -4

Answer 2

X-Y-4=0 is the correct answer

Just draw the graph of the axes and line with incilnation of 45 degrees cutting x axis at (4 , 0) sand y axis at (0 , y)

Now you know the slope is 1 since tan 45 is 1

The slope formula is (y2-y1)/(x2-x1)

Substitute X1 as 4

Y2 as y

X2 and Y2 as 0

Now you get y intercept as -4

Finally use y=mx+c (m is the slope is 1 and c is y intercept is -4)

So you get y=x-4

Final result after rearranging is x-y-4=0