Final answer:
The slope-intercept form of a tangent line to a curve at a given point, calculate the slope of the curve at that point, then use the point to find the y-intercept and form the equation y = mx + b.
Step-by-step explanation:
Finding the Slope-Intercept Form of a Tangent Line
To find the slope-intercept form of the equation of the tangent to a curve from parametric equations at a specific point (x,y), we need to identify the slope of the curve at that point and the y-intercept of the tangent line. If we are given a parabolic equation of the form y = ax + bx², where a and b are coefficients, and a = tan 00, b = (2(vocoso)²), we can use these to find the equation of the tangent line.
The slope of the curve at a given point is the derivative of the curve's equation at that point, which is the same as the slope of the tangent line. Once we have the slope (m), we can use the point (x,y) to solve for the y-intercept (b) in the slope-intercept form, which is y = mx + b. For linear equations, the coefficient of x represents the slope, and the constant term represents the y-intercept. To find the slope from two points, we calculate the difference in y-values divided by the difference in x-values. The strategy for solving includes finding the tangent at the specific point and then plugging in the known values to find the y-intercept.