To find the y-intercept of a linear equation, we simply need to put the equation into "slope-intercept" form. This will allow the y-intercept to be shown as the constant being added to the equation. To put a linear equation into slope-intercept form, we simply need to solve for Y. Let's do that.
-3x + 7Y = 21
3x + -3x + 7Y = 3x + 21
7Y = 3x = 21
(1 / 7) * 7Y = (3x + 21) * (1 / 7)
Y = (3x / 7) + (21 / 7)
Y = 3x/7 + 3
Now that we have the Y isolated, we can see the constant being added is 3. Hence, the y-intercept is (0,3) since by definition the y-intercept is the point at which the line crosses the x axis (where x = 0). If you plug x=0 into the equation, you get Y = 3.
