Question

The y-intercept of the line whose equation is 2x - 3y = 6 is
-2
3
6

Answer 1

y = -2

(first option listed)

Explanation:

a y-intercept is a point where the line crosses over the y-axis, which happens when x = 0.

So, the y-intercept is actually pretty each to find.

this is the easier way to find it: {plug directly into equation given}

2x - 3y = 6

(set x equal to 0)

[0] - 3y = 6

(divide both sides by -3)

y = -2

but you might have seen/ learned to solve the equation like this {to actually find the equation of the line and solve from that}

[this method is helpful to know/practice for when equations for functions get more complex]

2x - 3y = 6

+ 3y + 3y {add 3y to both sides}

2x = 3y + 6

-6 -6 {subtract 6 from both sides}

2x - 6 = 3y

÷3 ÷3 {divide both sides by 3 to isolate y}

`(2)/(3)x`
`- 2 = y` [flip sides of the equation]

`y=(2)/(3)x-2`

set x equal to 0 (x = 0)

y =
`(2)/(3) (0)` - 2

y = 0 - 2

y = -2

So, the y-intercept is -2.