Math Problem Statement
what’s the equation in slope intercept form
Solution
To find the equation of the tangent line in slope-intercept form, we need two pieces of information: the slope of the tangent line and the coordinates of the point where the tangent line touches the curve.
We already have the slope of the tangent line at , which is .
Next, we need the coordinates of the point on the curve where . We can find the -coordinate by substituting into the original function:
So, the point of tangency is .
Now we can use the point-slope form of the equation of a line:
where is the point of tangency and is the slope .
Therefore, the equation of the tangent line in slope-intercept form is:
Would you like further details or have any questions?
Here are 5 related questions you might want to ask:
- How do you convert from point-slope form to slope-intercept form?
- What is the significance of the y-intercept in the equation of a line?
- Can you explain how to find the equation of a tangent line for other types of functions?
- How does the slope of a tangent line relate to the derivative of the function?
- What are some applications of finding tangent lines in real-world problems?
Tip: When finding the equation of a tangent line, always ensure that you correctly identify the slope and the coordinates of the point of tangency.
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Math Problem Analysis
Mathematical Concepts
Equation of a Line
Point-Slope Form
Slope-Intercept Form
Formulas
Point-Slope Form
Slope-Intercept Form
Theorems
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Suitable Grade Level
Grades 9-12