Hi,   

Note: the standard slope-intercept form for an equation of a line is y = mx + b  

where m is the slope and b the y-intercept. 

a) State the value of a and of b.     

y = ax + 7 is parallel to the line y = 2x - 3  (lines have same slope)

    a = 2    y = 2x + 7

The line y = bx + 7 is perpendicular to the line y = 2x- 3.

Perpendicular lines have Slopes that are negative reciprocals of one another:

    b = -1/2    y = -.5x + 7

b) Calculate the perpendicular distance between the pair of parallel lines.

graphing 

y = 2x - 3 and y = 2x + 7 and the line perpendicular to both: y = -.5x + 7

Distance between Pt(0,7) and Pt(4,5)would be:













 

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