# Recent questions in Linear equations and graphs

Linear equations and graphs

### Regarding linear equations with one independent variable, answer the following questions: a. What is the general form of such an equation? b. In your expression in part (a), which letters represent constants and which represent variables? c. In your expression in part (a), which letter represents the independent variable and which represents the dependent variable?

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle\frac{{x}}{{3}}=\frac{{x}}{{2}}-{2}$$

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle\frac{{x}}{{5}}-\frac{{1}}{{2}}=\frac{{x}}{{6}}$$

Linear equations and graphs

### You work at the local pool as a lifeguard and you also work in the snack bar. You earn $15 per hour lifeguarding and$8 per hour working in the snack bar. Last week you worked a total of 20 hours and earned \$202. a. Write an equation in standard form for the hours you worked. b. Write an equation in standard form for the money you earned. c. Graph both equations on the same coordinate plane. d. Determine how many hours you worked as a lifeguard and how many hours you worked in the snack bar. Explain your reasoning.

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\frac{3x}{5}-x=\frac{x}{10}-\frac{5}{2}$$

Linear equations and graphs

### A student doing a Science Fair experiment put a hot bowl of soup in the refrigerator and checked the temperature of the soup every 2 minutes: a) Create a model describing how the soup cools. Be sure to look at the residuals to verify that your model is appropriate. b) Explain what the two values in the equation suggest about the soup. c) Estimate the temperature of the soup after 3 minutes. d) Estimate the temperature of the soup after 25 minutes. e) How much confidence do you place in those estimates? Why?

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle{20}-{\left(\frac{{x}}{{3}}\right)}=\frac{{x}}{{2}}$$

Linear equations and graphs

### $$\displaystyle{y}={3}+\sqrt{{{y}^{{2}}-{5}}}$$

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle\frac{{x}}{{2}}={\left({3}\frac{{x}}{{4}}\right)}+{5}$$

Linear equations and graphs

### $$\displaystyle{15}=-{6}-{\left({3}\frac{{p}}{{8}}\right)}$$

Linear equations and graphs

### Find the point on the line $$y = 5x + 2$$ that is closest to the origin.

Linear equations and graphs

### Use this graph to find a number of g such that

Linear equations and graphs

### Use the given graph of $$f(x) = x^2$$ to find a number $$(\delta)$$ such that if $$|x - 1| < (\delta)$$ then $$|x^2-1| < \frac{1}{2}$$ (Round your answer down to three decimal places.) $$(\delta) =$$

Linear equations and graphs

### find the area of the largest rectangle that can be inscribed in the ellipse $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle\frac{{x}}{{4}}={2}\frac{{{x}-{3}}}{{3}}$$

Linear equations and graphs

### Find the area of the surface. $$z = \frac{2}{3}(x\frac{3}{2} + y\frac{3}{2})$$ , $$0 \leq x \leq 1, 0 \leq y \leq 1$$

Linear equations and graphs

### Where is the greatest integer function $$f(x) =[[x]]$$ not differentiable? Find a formula for f’ and sketch its graph.

Linear equations and graphs

### Contain linear equations with constants in denominators. Solve each equation. $$\displaystyle\frac{{{x}+{1}}}{{3}}={5}-\frac{{{x}+{2}}}{{7}}$$

Linear equations and graphs