If an equation has no solution, and you graph both sides of the equation, how many points of intersection will the graphs have?
a. infinitely many b. none c. one d. two

The answer is (B). none.

Step-by-step explanation:  We are given that an equation has no solution. We are asked to find the number of points of intersection in the graph if we graph both sides of the equation.

Let us consider the following system of equations:

We graph both sides of the equation in the attached figure. We can easily see that the straight lines will never intersect each other.

Therefore, there will be no point of intersection in the graph.

Thus, the correct option is (B).

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

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step-by-step explanation: