Determine Point of Tangency & Value of "b" for y=8x+b

In summary, the point of tangency for the equation y=8x+b represents the point of intersection between the line and the curve. To determine the value of "b", you can use the coordinates of the point of tangency or the slope-intercept form of the equation. There can only be one point of tangency for y=8x+b due to the constant slope of 8. The value of "b" represents the y-intercept of the line and changing its value will shift the graph of y=8x+b up or down.
  • #1
phyico
5
0
The line y = 8x + b is tangent to the curve y = 2x^2.

Determine the point of tangency and the value of "b"
 
Physics news on Phys.org
  • #2
What does the number 8 in y = 8x + b represent?
 

1. What is the point of tangency for the equation y=8x+b?

The point of tangency for this equation is the point where the line y=8x+b touches the curve of any given function. This point represents the point of intersection between the line and the curve.

2. How do you determine the value of "b" for y=8x+b?

To determine the value of "b", you need to know the coordinates of the point of tangency. You can then substitute these coordinates into the equation y=8x+b and solve for b. Alternatively, you can use the slope-intercept form of the equation (y=mx+b) and substitute the slope value (8) and the coordinates of the point of tangency into the equation to solve for b.

3. Can there be multiple points of tangency for y=8x+b?

No, there can only be one point of tangency for y=8x+b. This is because the line y=8x+b is a straight line with a constant slope of 8, so it can only intersect the curve at one point.

4. What does the value of "b" represent in the equation y=8x+b?

The value of "b" represents the y-intercept of the line y=8x+b. This means that when x=0, the value of y will be equal to b. In other words, the line will intersect the y-axis at the point (0,b).

5. How does changing the value of "b" affect the graph of y=8x+b?

Changing the value of "b" will shift the graph of y=8x+b up or down, depending on whether b is positive or negative. For example, if b is positive, the graph will shift upward, and if b is negative, the graph will shift downward. The slope of the line will remain the same at 8, but the y-intercept will change accordingly.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
431
  • Calculus and Beyond Homework Help
Replies
11
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
122
  • Precalculus Mathematics Homework Help
Replies
18
Views
1K
  • Calculus and Beyond Homework Help
Replies
10
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
8
Views
466
  • Calculus and Beyond Homework Help
Replies
5
Views
726
  • Calculus and Beyond Homework Help
Replies
6
Views
735

Back
Top