Question

The points (6, −2) and (h, −3) fall on a line with a slope of 1. What is the valu
h =

Answer 1

Answer: h = 5

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Step-by-step explanation:

m = 1 is the given slope

(x1,y1) = (6,-2) and (x2,y2) = (h,-3) are the two points on a line of slope 1.

Let's use the slope formula to find h

`(x_1,y_1) = (6,-2) \text{ and } (x_2,y_2) = (h,-3)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\1 = (-3 - (-2))/(h - 6)\\\\1 = (-3 + 2)/(h - 6)\\\\1 = (-1)/(h-6)\\\\1(h-6) = -1\\\\h-6 = -1\\\\h = -1+6\\\\h = 5`

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The point (h,-3) updates to (5,-3).

The slope of the line through (6,-2) and (5,-3) is 1.

Use the slope formula to confirm this.

`(x_1,y_1) = (6,-2) \text{ and } (x_2,y_2) = (5,-3)\\\\m = (y_(2) - y_(1))/(x_(2) - x_(1))\\\\m = (-3 - (-2))/(5 - 6)\\\\m = (-3 + 2)/(5 - 6)\\\\m = (-1)/(-1)\\\\m = 1\\\\`

The answer is confirmed.