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