- #1
phyico
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The line y = 8x + b is tangent to the curve y = 2x^2.
Determine the point of tangency and the value of "b"
Determine the point of tangency and the value of "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.
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.
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.
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).
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.