# CPI Precalculus: Extra Practice on Linear Equations Worksheet 2

• Class: CPI Precalculus
• Author: Peter Atlas
• Text: Advanced Mathematics, Brown

1. Find an equation for the line described:
1. passes through (-3, -1) and has a slope 4.
2. Solution $$y + 1 = 4(x + 3)$$
3. passes through $$\displaystyle \left( \frac{5}{2}, 0 \right)$$ and has a slope $$\displaystyle \frac{1}{2}.$$
4. Solution $$\displaystyle y = \frac{1}{2} \left( x - \frac{5}{2} \right)$$
5. has x-intercept 6 and y-intercept 5
6. Solution $$\displaystyle \frac{x}{6} + \frac{y}{5} = 1$$
7. has x-intercept -2 and slope $$\displaystyle \frac{3}{4}.$$
8. Solution $$\displaystyle y + 2 = \frac{3}{4}x$$
9. passes through (1, 2) and (2, 6).
10. Solution $$y - 2 = 4(x - 1)$$
11. passes through (-7, -2) and (0, 0).
12. Solution $$\displaystyle y = \frac{2x}{7}$$
13. passes through (-3, 4) and is parallel to the x-axis.
14. Solution $$y = 4$$
15. passes through (-3, 4) and is parallel to the y-axis.
16. Solution $$x = -3$$
2. Determine whether each pair of lines is parallel, perpendicular, or neither
1. $$3x - 4y = 12$$ and $$4x - 3y = 12$$
2. Solution Neither
3. $$y = 5x - 16$$ and $$y = 5x + 2$$
4. Solution Parallel
5. $$5x - 6y = 25$$ and $$6x + 5y = 0$$
6. Solution Perpendicular
7. $$x = 8y + 3$$ and $$\displaystyle 4y - \frac{x}{2} = 32$$
8. Solution Parallel
3. Find the equation of the line described. Write your $$ANSWER$$ in standard form:
1. is parallel to $$2x - 5y = 10$$ and passes through (-1, 2).
2. Solution $$2x - 5y = -12$$
3. is perpendicular to $$4y - 3x = 1$$ and passes through (4, 0).
4. Solution $$4x + 3y = 16$$
5. is perpendicular to $$x - y + 2 = 0$$ and passes through (3, 1).
6. Solution $$x + y = 4$$
7. is parallel to $$3x - 5y = 25$$ and has the same y-intercept as the line $$6x - y + 11 = 0$$.
8. Solution $$3x - 5y = -55$$
4. Find the slope of the line passing through the two points (3, 9) and $$(3 + h, (3 + h)^2)$$.
5. Solution $$6 + h$$
6. Find the slope of the line passing through the two points $$(x, x^2)$$ and $$(x + h, (x + h)^2)$$.
7. Solution $$2x + h$$
8. Find the linear function satisfying the given conditions :
1. $$f(-1) = 0$$ and $$f(5) = 4$$.
2. Solution $$\displaystyle y = \frac{2}{3}(x + 1)$$
3. f(3) = 2 and f(-3) = -4
4. Solution $$y - 2 = x - 3$$
5. $$g(0) = 0$$ and $$g(1) = \sqrt{2}.$$
6. Solution $$y = \sqrt{2}x$$
7. The graph passes through the points (2, 4) and (3, 9).
8. Solution $$y - 4 = 5(x - 2)$$
9. $$\displaystyle f \left( \frac{1}{2} \right) = -3$$, and the graph of $$f$$ is a line parallel to the line $$x - y = 1$$.
10. Solution $$\displaystyle y + 3 = x - \frac{1}{2}$$
11. $$g(2) = 1$$ and the graph of $$g$$ is perpendicular to the line $$6x - 3y = 2$$
12. Solution $$\displaystyle y - 1 = -\frac{1}{2}(x - 2)$$