Practice with Graphs and  Equations of  Lines Topic Index | Algebra Index | Regents Exam Prep Center

 Answer the following questions dealing with equations and graphs of straight lines.
 1. Which of the following equations passes through the points (2,1) and (5,-2)? Choose: y = -x + 3 y = -x+2 Explanation Find the slope first.  (-2-1)/(5-2) = -1 Using the point (2,1) [you could also use (5,-2)] y-1 = -1(x-2) y-1 = -x+2 y = -x + 3

 2. Does the graph of the straight line with slope of -2 and y-intercept of -3 pass through the point (5,-13)? Choose: Yes No Explanation The equation is y = -2x -3 Substitute (5,-13) to see if it lies on the line. -13 = -2(5) - 3   True

 3. The slope of this line is 3/2. Choose: True False Explanation Remember SkiBird. You would be skiing downhill on this line. The line has a negative slope. So the positive slope answer is wrong.

 4. What is the slope of the line 3x + 2y = 12? Choose: 3                2 Explanation Be sure to put the equation into "y=" form. 3x+2y=12 2y=-3x+12 y=(-3/2)x+6 Slope = -3/2

 5. Which is the correct slope of the line through (-2,3) and (4,-5)? Choose: Explanation (Change in y values)/(change in x values) ((-5-3)/(4-(-2)) -8/6 -4/3

6.

 x 1 3 5 7 y 2 5 8 11

What is the slope of the line shown in the chart above?

Choose:

1
3

 7. The slope of this line is 1/2. Choose: True False Explanation Using RISE over RUN, you can count that the slope is over two and up one. This gives a RISE over RUN of 1 over 2 or 1/2. TRUE

 8. Does the line 2y + x = 7 pass through the point (1,3)? Choose: Yes No Explanation Substitute the x = 1 and y=3 into the equation to see if they make the equation true. 2(3) + 1 = 7 is true.

 9. Which is the equation of a line whose slope is undefined? Choose: x = -5 y = 7 x = y x + y = 0 Explanation Vertical lines have undefined slope. x=-5 is a vertical line. The slope of y = 7 is zero. The slope of x = y is one. The slope of x + y = 0 is negative one.

 10. Which is the equation of a line that passes through the point (2,5) and has a slope of -3? Choose: y = -3x - 3 y = -3x + 17 y = -3x + 11 y = -3x + 5 Explanation Use point slope formula. y - 5 = -3 ( x - 2 ) y - 5 = -3 x + 6 y = -3 x + 11

 11. What is the equation of this line? Choose: y = 2x - 3 y = -2x - 3 Explanation The y-intercept is -3. By counting, you can see that the slope is 2 over 1 (RISE/RUN). Using y = mx +b, the answer is y = 2x - 3.

 12. Which of these equations represents a line parallel to the line 2x + y = 6? Choose: y = 2x + 3 y - 2x = 4 2x - y = 8 y = -2x + 1 Explanation Lines that are parallel have the same slope. The slope of the given line is -2. Choice 4 is the only line whose slope is -2.  The others all have slopes equal to 2.

 13. What is an equation for the line that passes through the coordinates (2,0) and (0,3)? Choose: Explanation Find the slope first.  (0 - 3)/(2 - 0) = -3/2 Using the point (0,3) which is the y-intercept, b. y = mx + b y = (-3/2)x + 3

 Topic Index | Algebra Index | Regents Exam Prep Center Created by Donna Roberts