Substitute $y = 0$ into the equation to find the $x$-coordinate of $A$, and substitute $x = 0$ to find the $y$-coordinate of $B$.

Once you know $A(x_1, y_1)$ and $B(x_2, y_2)$, use the distance formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ to find the distance between them.

In Desmos, enter y = (3/4)x + 9. Then tap where the line crosses the $x$-axis and the $y$-axis; Desmos will display the coordinates of these intersection points (your points $A$ and $B$). Write down those coordinates.

Suppose your intercepts are $A(x_1, y_1)$ and $B(x_2, y_2)$ from the graph. In a new expression line, type sqrt((x2 - x1)^2 + (y2 - y1)^2) but replace x1, y1, x2, y2 with the actual numbers you wrote down. The value Desmos shows is the distance between $A$ and $B$.

Point $A$ is where the line crosses the $x$-axis, so its $y$-coordinate is 0. Point $B$ is where the line crosses the $y$-axis, so its $x$-coordinate is 0.

So:

• For point $A$, use $y = 0$ in the equation.
• For point $B$, use $x = 0$ in the equation.

Set $y = 0$ in the equation $y = \tfrac34 x + 9$ and solve for $x$:

So point $A$ is $(-12, 0)$.

Set $x = 0$ in the equation $y = \tfrac34 x + 9$ to get the $y$-intercept:

So point $B$ is $(0, 9)$.

Now use the distance formula between $A(-12, 0)$ and $B(0, 9)$:

Since $\sqrt{225} = 15$, the distance between points $A$ and $B$ is 15.