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The line through (-6,-5) and (6,6). The line through (1,10) and (-10,22).

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Final answer:

The equation of the line through (-6,-5) and (6,6) is y = (11/12)x - 31/2. The equation of the line through (1,10) and (-10,22) is y = (12/-11)x + 122/11.

Step-by-step explanation:

The equation of a line can be determined using the formula y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, use the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. For the first line, the slope is (6 - (-5)) / (6 - (-6)) = 11 / 12. The equation of the line is y = (11/12)x + b. Substitute one of the points to find the value of b: -5 = (11/12)(-6) + b. Simplify and solve for b to get b = -31/2. Therefore, the equation of the first line is y = (11/12)x - 31/2.

Using the same process for the second line, the slope is (22 - 10) / (-10 - 1) = 12 / (-11). The equation of the line is y = (12/-11)x + b. Substitute one of the points to find the value of b: 10 = (12/-11)(1) + b. Simplify and solve for b to get b = 122/11. Therefore, the equation of the second line is y = (12/-11)x + 122/11.

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