Questions: (14) Which line is parallel to the line given below? [2] y = -(5/2) x - 7 (a) 2 x + 5 y = -5 (b) 2 x - 5 y = 30 (d) 5 x - 2 y = 8 (15) Which of the following lines is perpendicular to the equation given below? [2] y = -2 x + 8 (a) x + 2 y = 8 (b) x - 2 y = 6 (c) 2 x + y = 4 (d) 2 x - y = 1 (16) Which pair of lines are perpendicular? [2] (a) x - y = 7 and y = x + 3 (b) y = -4 x + 1 and 8 x + 2 y = -10 (c) y = -8 and y = 2 (d) x = 4 and y = -1 (17) Line m passes through the point (2, -7) and (4, -9). Line m is parallel to which line? [2] (a) y = -x + 2 (b) y = x - 9 (c) x = 5 (d) y = -1 (18) The line passing through which two ordered pairs would be perpendicular to the equation y = 4 x - 1 ? [2] (a) (1, -3) and (2, 1) (b) (-4, 7) and (-1, -5) (c) (-8, -4) and (0, -2) (d) (4, 2) and (8, 1)

Solution Steps

The given line is \( y = -\frac{5}{2}x - 7 \). The slope of this line is \( m = -\frac{5}{2} \).

For a line to be parallel, it must have the same slope. Let's find the slope of each option:

• Option (a): \( 2x + 5y = -5 \)

  Rearrange to slope-intercept form: \[ 5y = -2x - 5 \implies y = -\frac{2}{5}x - 1 \] Slope: \( m = -\frac{2}{5} \)

• Option (b): \( 2x - 5y = 30 \)

  Rearrange to slope-intercept form: \[ -5y = -2x + 30 \implies y = \frac{2}{5}x - 6 \] Slope: \( m = \frac{2}{5} \)

• Option (d): \( 5x - 2y = 8 \)

  Rearrange to slope-intercept form: \[ -2y = -5x + 8 \implies y = \frac{5}{2}x - 4 \] Slope: \( m = \frac{5}{2} \)

The slope of the given line is \( -\frac{5}{2} \). None of the options have this slope, but we are looking for a line with the same slope, which is not present in the options. However, if we consider the negative reciprocal for perpendicularity, the correct option should have been \( m = \frac{5}{2} \), which is option (d).

Final Answer