Question

Match the linear equations with their x- and y - intercepts

Answer 1

1) (2,0) and (0,-1)

2) (-7/3,0) and (0,7/3)

3) (3,0) and (0,-21)

4) (-20/3,0) and (0,4)

Explanation:

The equation of the line has the form:

y=mx+b

Where m is the slope and b is the y intercept.

Then, you must solve for y in each equation to know the y-intecept.

To know the x-intercept you must substitute y=0 into each equation and solve for x. Therefore:

1)
`x-2y=2\\-2y=-x+2\\y=(1)/(2)x-1`

Then: b=-1

When y=0

`0=(1)/(2)x-1\\1*2=x\\x=2`

Answer: (2,0) and (0,-1)

2)
`-3x+3y=7\\3y=3x+7\\y=x+(7)/(3)`

Then b=7/3

When y=0

`0=x+(7)/(3)\\x=-(7)/(3)`

Answer: (-7/3,0) and (0,7/3)

3)
`7x-y=21\\y=7x-21`

b=-21

When y=0

`0=7x-21\\7x=21\\x=3`

Answer: (3,0) and (0,-21)

4)
`3x-5y=-20\\5y=3x+20\\y=(3)/(5)x+4`

b=4

When y=0

`0=(3)/(5)x+4\\3x=(-4)(5)\\x=-(20)/(3)`

Answer: (-20/3,0) and (0,4)