Find the points at which the line ax+by+c=0 crosses the x and y-axes. Assume that a≠0 and b≠0.

Cale Terrell

Cale Terrell

Answered question

2022-10-28

Find the points at which the line a x + b y + c = 0 crosses the x and y-axes. Assume that a 0 and b 0.
solve the equation a x + b y + c = 0 for y:
a x + b y + c = 0
a x + b y = c
b y = a x c
y = a x c b
x = 0 at y-intercept,
y = a ( 0 ) b c b
y = c b
The point at which the line crosses the y-axis is ( 0 , c b )
Now we solve the equation a x + b y + c = 0 for x:
a x + b y + c = 0
a x + b y = c
a x = b y c
x = b y c a
y = 0 at x-intercept
x = b ( 0 ) a c a
x = c a
The point at which the line crosses the x-axis is ( c a , 0 )

Answer & Explanation

Amadek6

Amadek6

Beginner2022-10-29Added 21 answers

Take advantage of what you already know:
- the x intercept is the value of 𝑥 when y = 0, and
- the y intercept is the value of 𝑦 when x = 0.
- a x + b y + c = 0 a x + b y = c
x intercept
We can use a x + b y = c to solve for x when y = 0, by plugging in 0 for y , , right at the start:
a x + b y y = 0 = c a x = c x = c a
y intercept
And we can do the same to solve for 𝑦 when x = 0, by plugging in 0 for x , right at the start:
a x x = 0 + b y = c b y = c y = c b
Martin Hart

Martin Hart

Beginner2022-10-30Added 3 answers

Easier way is this equation of line intercept form
x a + y b = 1
so write the given equatio in this form
a x + b y + c = 0
a x + b y = c
a x c + b y c = 1
x c a + y c b = 1
So intercept at X axis is ( c a , 0 ) and Y axis is ( 0 , c b )

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