Answer:
A
Step-by-step explanation:
To write the equation of the line. first calculate the slope using the slope formula.
Since the slope of this line is 0, it is horizontal and has the form y=b where b is the y-coordinate. So y = 2 is the equation. In general form, it would be y-2 = 0
To give you a context on the problem, a tangent line is a line that intersects the parabola only at one single point. A parabola is a curve that forms an arc-shaped figure. A tangent line to a parabola is shown in the attached picture.
Now, we apply the concepts in calculus and analytical geometry. The first derivative of the equation is equal to the slope at the point of intersection. This slope must be equal to the slope of the tangent line.
y = x² - 5x + 7
dy/dx = slope = 2x -5
Since tangent lines must have the same slope with what they intersect with, we can determine the slope from the equation: y = 3x + c. This is already arranged in a slope-intercept form, where 3 is the slope and c is the y-intercept. So, we can equate the equation above to 3.
2x - 5 = 3
x = 4
Now, we substitute x=4 to the original equation of the parabola:
y = (4)² - 5(4) + 7
y = 3
Therefore, the point of intersection is at (4,3). Now, we use it to the equation of the tangent line to find c.
y = 3x + c
3 = 3(4) + c
c = -9
You want 3 loaves of bread, at $1.50 a piece and a jar of jelly, at $4. So set up the equation 3(1.5)+1(4). You don't want peanut butter so that's unnecessary information. Your total is $8.50, so subtract that from 10, you get 1.5. You will have $1.50 left over.
