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1. Answer:

   To write an equation for a line, you can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept (the point at which the line crosses the y-axis).

   To find the slope of a line given two points, you can use the following formula:

   m = (y2 – y1) / (x2 – x1)

   where (x1, y1) and (x2, y2) are the coordinates of the two points.

   Using this formula, you can find the slope of Line A by plugging in the coordinates of the two points:

   m = (14 – 4) / (6 – 1) = 10/5 = 2

   You can then use the slope-intercept form of a linear equation to write the equation for Line A:

   y = 2x + b

   To find the y-intercept, you can plug in the coordinates of one of the points (1, 4) and solve for b:

   4 = 2 * 1 + b

   b = 2

   The equation for Line A is therefore:

   y = 2x + 2

   You can use the same process to find the equation for Line B. The slope of Line B is:

   m = (23 – (-2)) / (6 – 1) = 25/5 = 5

   Using the slope-intercept form of a linear equation, you can write the equation for Line B as:

   y = 5x + b

   To find the y-intercept, you can plug in the coordinates of one of the points (1, -2) and solve for b:

   -2 = 5 * 1 + b

   b = -7

   The equation for Line B is therefore:

   y = 5x – 7

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