If the point $(-2, 5)$ is on the graph of a function $y = f(x)$, what information does this give us about solving an equation?

The solution to $f(x) = 5$ is $x = -2$.

The solution to $f(x) = -2$ is $x = 5$.

The solution to $f(x) = 0$ is $x = 3$.

The solution to $f(x) = x$ is $x=5$.

Solving Equations and Inequalities by Graphing Practice — Grade 11 math

Lesson 5: Solving Equations and Inequalities by Graphing — Practice Questions

1. The point $(3, 11)$ is on the graph of $y = 2x + 5$. Using this graph, the solution to the equation $2x + 5 = 11$ is $x = \_\_\_$.
2. The graph of $y = 4x - 1$ contains the point $(2, 7)$. What is the solution set for the inequality $4x - 1 > 7$?
- A. $x > 2$
- B. $x < 2$
- C. $x > 7$
- D. $x < 7$
3. If the point $(-2, 5)$ is on the graph of a function $y = f(x)$, what information does this give us about solving an equation?
- A. The solution to $f(x) = 5$ is $x = -2$.
- B. The solution to $f(x) = -2$ is $x = 5$.
- C. The solution to $f(x) = 0$ is $x = 3$.
- D. The solution to $f(x) = x$ is $x=5$.
4. The graph of the line $y = 6 - x$ is used to solve an inequality. If the solution is found to be $x < 4$, the original inequality was $6 - x > \_\_\_$.
5. On the graph of $y = -3x + 8$, the point $(3, -1)$ is present. Based on this, the solution to the inequality $-3x + 8 < -1$ is $x > \_\_\_$.
6. To solve the equation $4x - 3 = -x + 7$ by graphing, you graph $y = 4x - 3$ and $y = -x + 7$. What does the x-coordinate of their intersection point represent?
- A. The solution to the equation
- B. The y-intercept of the first line
- C. The slope of the second line
- D. The y-coordinate of the solution
7. The graphs of $y = 3x + 1$ and $y = -2x + 11$ are used to solve an equation. If the lines intersect at the point $(2, 7)$, what is the solution to the original equation? $x = \_\_\_$
8. Which pair of functions should be graphed to find the solution for the equation $5x - 4 = 2x + 5$?
- A. $y = 5x - 4$ and $y = 2x + 5$
- B. $y = 5x$ and $y = 2x$
- C. $y = 3x$ and $y = 9$
- D. $y = 7x$ and $y = 1$
9. To solve the equation $-x + 8 = 4x - 2$, the functions $y = -x + 8$ and $y = 4x - 2$ are graphed. Their intersection point is $(2, 6)$. The solution is $x = \_\_\_$.
10. The graphs of $y = 3.5x + 2$ and $y = 1.5x + 8$ intersect at the point $(3, 12.5)$. What is the solution to the equation $3.5x + 2 = 1.5x + 8$? $x = \_\_\_$