Line M has a y-intercept of 4, and its slope must be an integer-multiple of 1/7 Given that - Maths - Straight Lines

Question

Line M has a y-intercept of –4, and its slope must be an
integer-multiple of 1/7 Given that Line M passes below (4,
–1) and above (5, –6), how many possible slopes could
Line M have?
​

Shivam Mishra · Accepted Answer

Dear Student,
Please find below the solution to the asked query:

Well, for starters, zero is a multiple of every number, and a line with slope zero, the horizontal line y = –4 passes below 4,-1 and above 5, –6
 That horizontal line is our starting point
The point 4, –1 is over 4, up 3 from the y-intercept 0, –4
 A line with a slope of 34 would go straight from 0, –4 to 4, –1
 Thus, we need a slope that is less than 34
 Notice that 34= 2128
 Notice that 57 = 2028  so this would be less than 34
 Therefore, 17 through 57 will all slope up, obviously above 5, –6, and all will pass below 4, –1
 That’s five upward sloping lines
  The point 5, –6 is over 5, down 2, from the y-intercept 0, –4
 A line with a slope of –25 would go straight from 0, –4 to 5, –6
 Thus, we need a slope that is more than –25; another way to say that is, we need a negative slope whose absolute value is less than 25
 Well,25 = 1435, while 27= 1035 and 37 = 1535, so 27 <25 <37 
 The negatively sloping lines obviously pass below 4, –1, but only two of them, –17 and –27, pass above (5, –6
  That’s one horizontal line, five upward sloping lines, and two downward sloping lines, for a total of eight
 Answer is 8

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Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7. Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have? ​

Line M has a y-intercept of –4, and its slope must be an integer-multiple of 1/7. Given that Line M passes below (4, –1) and above (5, –6), how many possible slopes could Line M have?