Lines Here are some equations of straight lines: 1
3
y = x + 4
! 4
y=8x–3 3
y = x − 4 ! 2
2y+x=4 Name______________________________________ y+4x+6 = 0 3y=2x–8 y + 6x =11 y=6x-­‐4 y=4x+4 3
y = 4x + 2
!
Here are some properties of equations: These lines are parallel These lines are These lines have the These lines have the perpendicular same y-­‐intercept same x-­‐intercept 1. Find two equations to match each of the properties. 2. What is the slope of the line joining the points (2,5) and (7,15)? 3. Give the coordinates of two points for which the slope of the line between them is 3. 4. a. Give an equation of a line with a slope of 3. b. Keeping the same equation, write it in a different way. 5. What is the y-­‐intercept of the line y=3x+7? 6. What is the x-­‐intercept of the line 2y=3x-­‐6? 7. What would be the slope of a line perpendicular to y=2x+4? 8. Give the equations of two lines that are perpendicular to each other. Here are some equations of straight lines: y+2x=8 2y=x–4 2y+½x+1=0 y+2x+2=0 4y–x=1 y=½x+2 9. Which four lines form the four sides of a rectangle? These lines go through the point (1,5) y=x–4 y=4–x y=2(x–1) 2y=4–x Explain your reasoning carefully. 10. Complete the drawing to show the four lines and the x-­‐ and y-­‐axes. Label the lines clearly. 11. Line segment SP has equation y = 2x + 3. Find the equations of the line segments forming the other three sides of the rectangle. 12. Find the equation of a line passing through the origin and parallel to the line 2x – y = 5. 13. If the equation of a line p in the coordinate plane is y = 3x + 2, what is the equation of line q which is a reflection of line p in the x-­‐axis? 14. If the slope of a line is ½ and the y-­‐intercept is 3, what is the x-­‐intercept of the same line? ( ) ( )
15. The vertices of the triangle PQR are the points P 1,2 , Q 4,6 , and R ( −4,12) . Which one of the following statements about triangle PQR must be true? a. PQR is a right triangle with the right angle at P. b. PQR is a right triangle with the right angle at Q. c. PQR is a right triangle with the right angle at R. d. PQR is not a right triangle. Justify your answer. 16. Prove that the slopes of two parallel lines are equal. 17. Prove that the slopes of two perpendicular lines have a product of –1.