Can someone please check my work for me?

Write an equation of the line satisfying the given conditions.
9) Intersects the line y = 2 + 3x at infinitely many places. 9)
A) y = -3x + 2 B) y = 2x + 3 C) y = -1/3x + 2 D) y = 2 + 3x
Is the answer A

Use the discriminant to determine how many real-number solutions the equation has.
11) 1 - 7a2 = -7a - 2 11)
A) 2 B) 1 C) 0
Is the answer B

Determine the number of real-number solutions to the equation from the given graph.
14) 5x2 + 4x + 6 = 0, given the graph of y = 5x2 + 4x + 6
A) 1 B) 0 C) 3 D) 2
Is the answer A

number 9 is D

To check your work for the first question, you need to determine the equation of the line that intersects the line y = 2 + 3x at infinitely many places.

To do this, you can recognize that any equation of the form y = 2 + 3x will intersect y = 2 + 3x at every point along the line. Therefore, the correct answer is D) y = 2 + 3x, so your answer is correct.

To determine the number of real-number solutions to the equation using discriminant, you need to consider the equation 1 - 7a^2 = -7a - 2.

The discriminant (denoted as Delta) is calculated as Delta = b^2 - 4ac, where a, b, and c are coefficients of the equation in the form ax^2 + bx + c = 0.

In this case, we have a = -7, b = 7, and c =-2. So, the discriminant becomes Delta = (7)^2 - 4(-7)(-2) = 49 - 56 = -7.

If the discriminant is less than 0, as it is in this case, the equation has no real-number solutions. Therefore, the correct answer is C) 0, so your answer is incorrect.

To determine the number of real-number solutions to the equation from the given graph, you need to find the number of times the graph of the function y = 5x^2 + 4x + 6 crosses the x-axis.

Looking at the graph of y = 5x^2 + 4x + 6, you need to observe the points where the graph intersects or touches the x-axis. The number of times this happens represents the number of real-number solutions to the equation.

In this case, the graph touches or intersects the x-axis at only one point. Therefore, the correct answer is A) 1, so your answer is correct.