What are the x- and y-intercepts for the equation "2x + 3y = 6"? (please show how you solved for it)

Answer 1

The y-intercept is where the line (or curve) crosses the y-axis. Notice the y-axis is also the vertical line x=0.

Set x=0 to find the y-intercept: 2(0) + 3y = 6 --> 3y = 6 --> 3y/3 = 6/3 ---> y=2

Similarly, the x-intercept is where the line or curve crosses the x-axis, and the x-axis correponds to the horizontal line y=0. Set y=0 to find the x-intercept. 2x + 3(0) = 6 --> x=3

Answer 2

Hi Sarah,

first, we are going to put the equation into the y = m x + b format because to get the x and y intercept we need to set x or y equal to 0. The intercept basically tells us where the line is crossing either the x or y axis.

So, let's begin,

2 x + 3 y = 6

2 x - 2 x + 3 y = 6 + -2 x ( using the additive inverse)

3 y = - 2 x + 6

we then divide everything by 3 so that the coefficient in front of the y is equal to 1.

y = -2/3 x + 2

Now let's get the intercepts

if y = 0 then

0= -2/3 x + 2 solving

-2 = - 2/3 x

multiplying each side by - 3/2 the multiplicative inverse we get

-3 = x

so the x intercept is -3.

Now for the y

we set x= 0

y= -2/3 (0) + 2

y= 2

so the y intercept is = 2

I hope this hopes.