The grid shows point T and line n.
Which equation best represents the point-slope form of the line that passes through point T and is parallel to line n?
line n starts at point 6,6 and ends at point -6,1
point T is at 3,-5
To find the equation of a line parallel to line n that passes through point T, we need to use the point-slope form of a line, which is given by the equation y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) are the coordinates of the point T.
First, let's find the slope of line n. The slope, denoted by m, is given by the formula m = (y2 - y1) / (x2 - x1). Using the coordinates of the endpoints of line n, we can calculate the slope:
m = (1 - 6) / (-6 - 6) = -5 / -12 = 5/12
Since we want to find the equation of a line parallel to line n, the slope of the new line will be the same, namely 5/12.
Now, we can substitute the coordinates of point T (3, -5) and the slope (5/12) into the point-slope form equation:
y - (-5) = (5/12)(x - 3)
Simplifying the equation, we have:
y + 5 = (5/12)x - 15/12
Rearranging the equation to the standard form, we get:
(5/12)x - y = 15/12 - 5
Multiplying through by 12 to eliminate fractions, we have:
5x - 12y = 15 - 60
Simplifying further, we get:
5x - 12y = -45
Therefore, the equation that represents the point-slope form of the line passing through point T and parallel to line n is:
5x - 12y = -45