Write down the formula for the slope of the line as M = (Y2 - Y1)/(X2 - X1), where M is the slope of the line, Y2 is the y-coordinate of a point called "A" on the line, X2 is the x-coordinate of point "A," Y1 is the y-coordinate of a point called "B" on the line and X1 is the x-coordinate of point B.
Substitute the value of the slope given and the given coordinate values of point A and point B. Use a slope of "1" and the coordinates of point A as (0, 0) for the point (X2, Y2) and the coordinates of point B as (1, Y1) for the other point (X1, Y1), where Y1 is the unknown coordinate that you must solve for. Check that after you substitute these values into the slope formula that the slope equation reads 1 = (0 - Y1)/(0 - 1).
Solve for the missing coordinate by algebraically manipulating the equation such that the missing coordinate variable is on the left side of the equation and actual coordinate value you must solve for is on the right side of the equation. Use the "Basic Rules of Algebra" link (see Resources) if you are not familiar with solving algebraic equations.
Observe that for this example, the equation, 1 = (0 - Y1)/(0 - 1), simplifies to 1 = -Y1/-1 since subtracting a number from 0 is the negative of the number itself. And so 1 = Y1/1. Conclude that the missing coordinate, Y1, is equal to 1, since, 1 = Y1 is the same as Y1 = 1.