The y-intercept is where a line crosses the y-axis, and on that axis x is zero — so it is one substitution and a one-step solve away. These free printable worksheets give a line in standard form and ask only for the y-intercept.
Setting x = 0 removes the x-term. For 3x + 4y = 24 the 3x is gone, leaving 4y = 24 and y = 6, so the line crosses at (0, 6). The one thing to keep straight is which variable to zero: the y-intercept is found by making x zero, not y, and a child who mixes the two finds the wrong crossing every time. This page holds the answer on the y-intercept so that pairing is drilled cleanly, while the combined sheet keeps both crossings in play at once.
Why this sheet works
These are standard-form lines on purpose. In y = mx + b the y-intercept is already printed as b, so reading it is copying a number; here the equation hides it behind a term that has to be cleared first, which is the difference between reading an intercept and finding one.
How this one works
One question from this sheet, worked through a step at a time.
the y-intercept of 3x − 2y = −18
3x − 2y = −18x = 0
−2y = −18
y = 9
The y-intercept is where the line crosses the y-axis, and there x = 0. Put x = 0 into 3x − 2y = −18.
The x-term disappears, leaving −2y = −18.
Divide by −2: −18 ÷ −2 = 9 — so the y-intercept is 9.
