Answer:
To find the equation of line d, which is parallel to line c and passes through the point (5, -7), we can use the fact that parallel lines have the same slope.
First, let's determine the slope of line c. The equation of line c is given as y - 6 = -7/6(x - 5). We can rewrite this equation in slope-intercept form (y = mx + b), where m represents the slope and b represents the y-intercept.
Starting with the equation of line c:
y - 6 = -7/6(x - 5)
Expanding the brackets:
y - 6 = -7/6x + 35/6
Rearranging to isolate y:
y = -7/6x + 35/6 + 6
y = -7/6x + 35/6 + 36/6
y = -7/6x + 71/6
Comparing this equation to y = mx + b, we can see that the slope (m) of line c is -7/6.
Since line d is parallel to line c, it will have the same slope. Therefore, the equation of line d can be written as:
y = (-7/6)x + b
To find the value of b, we can substitute the coordinates of the given point (5, -7) into this equation and solve for b.
-7 = (-7/6)(5) + b
-7 = -35/6 + b
To simplify this equation, we need to find a common denominator for -35 and 6. The least common multiple of 35 and 6 is 210. Multiplying both sides by 210, we get:
-1470 = -35(210)/6 + 210b
Simplifying further:
-1470 = -35(35) + 210b
-1470 = -1225 + 210b
Adding 1225 to both sides:
-1470 + 1225 = 210b
-245 = 210b
Dividing both sides by 210:
-245/210 = b
-7/6 = b
Therefore, the value of b is -7/6.
Substituting the values of m and b into the equation y = mx + b, we can write the equation of line d as:
y = (-7/6)x - 7/6
So, the equation of line d is y = (-7/6)x - 7/6.
Explanation: