Find the coordinates of the points A and B where the line 5x+y=10 cuts x-axis and y-axis respectively?

3 Answers
Feb 21, 2018

The x-intercept is Point A: (2,0).

The y-intercept is Point B: (0,10)

Explanation:

The line cuts the x-axis and y-axis at the x-intercept and the y-intercept.

X-intercept: value of x when y=0

Substitute 0 for y, and solve for x.

5x+0=10

5x=10

Divide both sides by 5.

x=10/5

x=2

Point A: (2,0) larr x-intercept

Y-intercept: value of y when x=0

Substitute 0 for x.

5(0)+y=10

Simplify.

0+y=10

y=10

Point B: (0,10) larr y-intercept

graph{5x+y=10 [-14.24, 14.23, -7.12, 7.12]}

Feb 21, 2018

x-axis A=(2,0)
y-axis B=(0,10);

Explanation:

5x+y=10 is the equation of a straight line.
When you want to find the intersection of a straight line with the axis you basically want to know what is the value of y when x is equal to 0 (y-axis intercection) and what is the value of x when y is equal to 0 (x-axis intecection).
x-axis:
when y=0 the equation becomes:
5x+0=10=>x=10/5=>x=2
so the first point is A=(2,0)

y-axis:
when x=0 the equation becomes:
0+y=10=>y=10
so the second point is B=(0,10)
graph{5x+y=10 [-10, 10, -5, 5]}

Feb 21, 2018

A(2,0)" and "B(0,10)

Explanation:

"to find where the line crosses the x and y axes"

• " let x = 0, in the equation for y-intercept"

• " let y = 0, in the equation for x-intercept"

x=0rArr0+y=10rArry=10larrcolor(red)"y-intercept"

y=0rArr5x+0=10rArrx=2larrcolor(red)"x-intercept"

"crosses x-axis at "A(2,0)" and y-axis at "B(0,10)
graph{(y+5x-10)((x-2)^2+(y-0)^2-0.04)((x-0)^2+(y-10)^2-0.04)=0 [-20, 20, -10, 10]}