the line passing through (7,y) and (1,0) is parallel to the joining line (4,4) and (-2,1) find y

The slope of the line passing through the two given points is 6/3 = 2

Your line with the unknown y must have the same slope. Therefore
(7-1)/(y-0) = 6/y = 2
y = 3

To find the value of y, we need to determine the slope of both lines and use the fact that parallel lines have the same slope.

The slope of the line passing through (7,y) and (1,0) can be found using the formula:

m1 = (y2 - y1) / (x2 - x1)

Substituting the given points (7, y) and (1, 0):

m1 = (0 - y) / (1 - 7)
= (-y) / (-6) (simplifying)

Now let's find the slope of the line joining the points (4,4) and (-2,1) using the same formula:

m2 = (y2 - y1) / (x2 - x1)

Substituting the given points (4, 4) and (-2, 1):

m2 = (1 - 4) / (-2 - 4)
= (-3) / (-6)
= 1/2 (simplifying)

Since parallel lines have the same slope, we can equate the two slopes:

(-y) / (-6) = 1/2

To solve for y, cross multiply:

-2y = -6(1)
-2y = -6
y = -6 / -2
y = 3

Therefore, the value of y is 3.

To find the value of y in the line passing through (7, y) and (1, 0) that is parallel to the line joining (4, 4) and (-2, 1), we need to determine the slope of the given line and then use it to find the equation of the new line.

The slope of the line joining two points (x1, y1) and (x2, y2) can be calculated using the formula:

slope = (y2 - y1) / (x2 - x1)

Let's first calculate the slope of the given line joining (4, 4) and (-2, 1):

slope = (1 - 4) / (-2 - 4) = -3 / -6 = 1/2

Now we can use this slope to find the equation of the new line passing through (7, y) and (1, 0).

The equation of a line can be written in the slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept.

Since the new line is parallel to the given line, it will have the same slope of 1/2. Therefore, the equation of the new line is:

y = (1/2)x + b

To find the value of b, we can substitute the coordinates of one of the points (1, 0) into the equation:

0 = (1/2)(1) + b
0 = 1/2 + b
b = -1/2

Now we have the equation for the new line as:

y = (1/2)x - 1/2

To find the value of y when x = 7, we can substitute x = 7 into the equation:

y = (1/2)(7) - 1/2
y = 7/2 - 1/2
y = 6/2
y = 3

Therefore, when the line passing through (7, y) and (1, 0) is parallel to the line joining (4, 4) and (-2, 1), y = 3.