60–62. {Use of Tech} Multiple tangent lines Complete the following steps. <IMAGE>
b. Graph the tangent lines on the given graph.
x+y³−y=1; x=1

Verified step by step guidance

1. First, identify the function given by the equation x + y³ - y = 1 and solve for y in terms of x to express it in a more usable form for graphing.
2. Next, differentiate the function implicitly with respect to x to find the derivative dy/dx, which represents the slope of the tangent line at any point on the curve.
3. Evaluate the derivative at the specific x-value of 1 to find the slope of the tangent line at that point.
4. Using the point-slope form of the equation of a line, y - y₁ = m(x - x₁), substitute the point (1, y₁) and the slope m to write the equation of the tangent line.
5. Finally, graph the original function and the tangent line on the same coordinate system to visualize how the tangent line touches the curve at the point of tangency.