In our previous post, we covered Desmos tips for SAT, specifically on using the Desmos SAT calculator to solve single-variable equations. In this post, we’ll dive into a more advanced topic: solving **single-variable equations with unknown constants**. Utilizing the Desmos SAT calculator and its slider tool, you can efficiently manage these problems on the Digital SAT, enhancing your overall **SAT math** performance.

## How to Solve Equations with Unknown Constants Using Desmos SAT

The problem below is one example of a single variable equation with an unknown constant. This single variable equation is a linear equation with an unknown constant “p.”

To Solve a Problem Like This

### Follow these steps:

**Enter the Equation**

Type the equation into Row 1 of the**Desmos SAT calculator**. Since this problem involves an unknown constant like “p,”**Desmos SAT**will prompt you to create a slider for it. Click the constant highlighted in blue to add the slider.

**Set the Slider Range**

Click to the left and right of the slider icon to adjust the slider range if needed. For this example question, the answer choices range from 0 to 4, so the default setting of -10 to 10 works well here.

**Check the Solutions**

Use the slider to check different values for the constant and see how they affect the graph. You can also set the slider to specific values. This is a great tactic on multiple choice questions like this one, because you can quickly check each answer choice by entering a precise value for “p.”

The correct answer is **Choice B**. When we set the slider equal to 1/7, the Desmos calculator does not produce any vertical lines. As we’ll remember from the last post, vertical lines indicate solutions. If Desmos produces no vertical lines when p = 1/7, that means that when p = 1/7, this equation has no solutions. The correct answer is therefore B, 1/7.

## See Desmos in Action: Solving Equations Made Simple

Check out this video where we demonstrate the step-by-step process of solving single-variable equations with unknown constants using the Desmos SAT calculator. Follow along to master the slider tool and efficiently tackle similar problems on your SAT:

## Additional Practice Problems with Desmos SAT

### Question 1: Solving a Quadratic Equation with an Unknown Constant

This problem features a quadratic equation with an unknown constant “c.” The approach for solving this quadratic equation with **Desmos SAT** remains similar to that of linear equations.

**Solution:**

Choice C is correct. The question asks us to identify the value of c for which the equation has one solution. Because this is a multiple choice question, we find the solution by plugging in each answer choice for “p.” -25 is the only value that produces one vertical line. Therefore Choice C must be correct:

### Question 2: Quadratic Equation with an Unknown “b” Value

This is a quadratic equation where we need to determine the value of “b”. This equation is not a multiple choice question, so it is probably best solved using a function

**Solution:**

The correct answer is **51**. Using **Desmos SAT**, replace the zero in the original equation with “y” to observe the graph. The equation has no solutions when **b = 52. **The problem states that the equation has no solutions. We can use the slider to see that the quadratic has no solutions whenever b is less than 52. The greatest integer value of b that yields zero solutions is therefore 51.

When b = 51, the function has no solutions, because it is an “open down” parabola with a vertex at (25.5, -25.75).

### Question 3: Single-Variable Linear Equation with Unknown “m”

For this linear equation, we need to test different values for “m” to identify the correct solution.

**Solution:**

The correct answer is **D** (3/2). The question indicates that the equation has one solution. Testing each answer choice in Desmos, we can see that every choice except for 3/2 produces one vertical line. Choice D does not produce a vertical line. This means that when m = 3/2, the equation has either infinite solutions or no solutions. With a bit of algebra we can see that when m = 3/2, the equation has no solutions. In either case, the answer is D, 3/2.

## Key Takeaways for SAT Math Success

**Desmos SAT Calculator**is an essential tool for solving equations with unknown constants.- Use the
**slider tool**to test different values quickly and find accurate solutions.

Remember, while Desmos helps with the calculations, a strong foundation in math is crucial for scoring high on the **SAT**.

## Looking Ahead: Desmos Tips for SAT, Part 3

In the next part of this series, we’ll explore how to solve **systems of equations** using **Desmos SAT**. This powerful tool will help you identify intersection points for multiple variables, providing another strategy to excel on the **SAT math** section.

## Prepare for the SAT with MentoMind

Ready for more practice with **Desmos SAT**? Check out **MentoMind**, where you can access over **3500+ practice questions** and **10 full-length digital SAT tests**. Our platform is designed to help you master the **Desmos calculator** and build the math skills you need for success.