Question

Directions: Answer each of the questions below.

1. Does the line 3y + x = 5 pass through the point (2, 7)?
2. What is the slope of the line x + 5y = 9?
3. Does the graph of the straight line with slope of -3 and y-intercept of -4 pass through the point (-2, 2)?
4. What is the slope of the line that passes through (-1, 4) and (3,- 8)?
5. Does the line y + 4x = 7 pass through the point (1, 3)?
6. True or False: 5x + 2y = 0 is the equation of a line whose slope is undefined.
7. True or False: 2y = -x + 5 is the equation of a line that passes through the point (1, 2) and has a slope of -1/2.
8. True or False: y = -3x + 4 is an equation that represents a line parallel to the line 3x + 2y = 9.
9. Does the graph of the straight line with slope of -5 and y-intercept of -8 pass through the point (2,-3)?
10. Write an equation that passes through the points (3, 6) and (1,-1).

Answer 1

1. No, the line passes through the point (2, 7).
2. The slope of the line is −1/5.
3. Yes, the line with a slope of -3 and y-intercept of -4 does not pass through the point (-2, 2).
4. The slope of the line is -3.
5. Yes, the line does not pass through the point (1, 3).
6. True, the equation 5x+2y=0 represents a line with an undefined slope.
7. False, the equation 2y=−x+5 does not have a slope of -1/2.
8. False, the equation y=−3x+4 does not represent a line parallel to 3x+2y=9.
9. No, the line with a slope of -5 and y-intercept of -8 passes through the point (2, -3).
10. y=(7/2)x-(33/2)

1. The equation 3y+x=5 can be tested by substituting the coordinates of the given point (2, 7). When 3(7)+2=21+2, the equation is false, confirming that the line passes through the point.
2. The slope of the line x+5y=9 is found by rearranging the equation into slope-intercept form (y=mx+b), where m represents the slope. The resulting slope is −1/5.
3. The line with a slope of -3 and y-intercept of -4 has the equation y=−3x−4. Substituting the coordinates of (-2, 2) into this equation results in 2=−3(−2)−4, which is true.
4. The slope between the points (-1, 4) and (3, -8) is calculated as the change in y divided by the change in x, yielding a slope of -3.
5. Testing the point (1, 3) in the equation y+4x=7 gives 3+4(1)=7, which is true. Thus, the line does pass through the point.
6. The equation 5x+2y=0 represents a line with an undefined slope because, when solved for y, it becomes y=− 5/2 x, and the coefficient of x is the slope.
7. The equation 2y=−x+5 does not have a slope of -1/2. When rewritten as y=− 1/2x+ 5/2, it is evident that the slope is -1/2.
8. The equation y=−3x+4 does not represent a line parallel to 3x+2y=9, as the slopes are different.
9. The line with a slope of -5 and y-intercept of -8 has the equation y=−5x−8. Substituting the point (2, -3) into this equation results in −3=−5(2)−8, which is false, indicating that the line does not passes through the given point.
10. To find the equation passing through the points (3, 6) and (1, -1), the slope (m) is calculated as the change in y divided by the change in x, yielding −7/2. Substituting one set of coordinates and the slope into the slope-intercept form (y=mx+b), the equation y=(7/2)x-(33/2) is derived.