{"id":42765,"date":"2025-06-29T10:13:20","date_gmt":"2025-06-29T10:13:20","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=42765"},"modified":"2025-06-29T10:13:21","modified_gmt":"2025-06-29T10:13:21","slug":"find-the-equation-of-the-tangent-line-and-use-desmos-to-draw-the-graph-of-x-y-and-the-tangent-line","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-equation-of-the-tangent-line-and-use-desmos-to-draw-the-graph-of-x-y-and-the-tangent-line\/","title":{"rendered":"Find the equation of the tangent line and use Desmos to draw the graph of (x, y) and the tangent line"},"content":{"rendered":"\n


Find the equation of the tangent line and use Desmos to draw the graph of (x, y) and the tangent line (save it to file and print). The equation is y = x^2 at x = 2 and y = 5 at x = 8. Also, find the equation y = zx^2 + vi + # at x = [<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To find the equation of the tangent line to the curve y=x2y = x^2y=x2 at the point where x=2x = 2x=2, let’s go through the steps in detail.<\/p>\n\n\n\n

Step 1: Find the slope of the tangent line<\/h3>\n\n\n\n

The slope of the tangent line is given by the derivative of the function y=x2y = x^2y=x2.<\/p>\n\n\n\n

The derivative of y=x2y = x^2y=x2 is: dydx=2x\\frac{dy}{dx} = 2xdxdy\u200b=2x<\/p>\n\n\n\n

At x=2x = 2x=2, substitute into the derivative: dydx=2(2)=4\\frac{dy}{dx} = 2(2) = 4dxdy\u200b=2(2)=4<\/p>\n\n\n\n

So, the slope of the tangent line at x=2x = 2x=2 is 444.<\/p>\n\n\n\n

Step 2: Find the point on the curve at x=2x = 2x=2<\/h3>\n\n\n\n

The point on the curve is given by substituting x=2x = 2x=2 into the original function: y=22=4y = 2^2 = 4y=22=4<\/p>\n\n\n\n

Thus, the point of tangency is (2,4)(2, 4)(2,4).<\/p>\n\n\n\n

Step 3: Use the point-slope form of the equation of a line<\/h3>\n\n\n\n

The point-slope form of the equation of a line is: y\u2212y1=m(x\u2212x1)y – y_1 = m(x – x_1)y\u2212y1\u200b=m(x\u2212x1\u200b)<\/p>\n\n\n\n

Where:<\/p>\n\n\n\n