Calculate the y-intercept of the graph of 2x-3y=18?

There is another way to write the same equation (looks different - carries the exact same information).

It is called the "slope-intercept" format, and it looks like this:

y = mx + c

where m and c are (normally) just numbers:

m is the slope (how fast y rises, when x rises by 1, and

c is the y-intercept (the value of y, when x=0)

Use the normal rules of equation manipulation to get there, from here:

2x - 3y = 18

multiply both sides (all terms) by -1

-2x + 3y = -18

add "2x" to both sides

3y = 2x - 18

divide both sides by 3

y = (2/3)x - 6

the slope = 2/3

the y-intercept = -6

To check, make x=0 and solve for y

y = (2/3)(0) - 6

y = -6

2x - 3y = 18

line

x-intercept | 9

y-intercept | -6

normal vector | (-2/sqrt(13), 3/sqrt(13))≈(-0.5547, 0.83205)

slope | 2/3≈0.666667

curvature | 0

2x - 3y = 18

You need to know that the y-intercept is where the graph crosses the y axis.

The y axis is the line where x = 0, so substituting that gives

2*0 - 3y = 18

y = -6

When x = 0, the y = -6.

Answer:  -6