Write an equation of the line passing through the point (13,-40) and parallel to the line passing the points (1,3) and (7,13). Write your answer in slope-intercept form.
y - -40 = 5/3 (x - 13)
y = 5/3 x - 185/3
To find the equation of a line parallel to another line, we first need to calculate the slope of the given line passing through the points (1,3) and (7,13).
The slope of a line is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the points (1,3) and (7,13):
m = (13 - 3) / (7 - 1)
m = 10 / 6
m = 5/3
Now that we have the slope of the given line, we can use the point-slope form of the equation of a line to find the equation of the line parallel to it. The point-slope form is given by:
y - y1 = m(x - x1)
Using the point (13,-40) and the slope 5/3:
y - (-40) = (5/3)(x - 13)
Simplifying the equation:
y + 40 = (5/3)(x - 13)
To write the equation in slope-intercept form (y = mx + b), we need to further simplify the equation:
y + 40 = (5/3)x - (5/3)(13)
y + 40 = (5/3)x - (65/3)
Rearranging the equation to solve for y:
y = (5/3)x - (65/3) - 40
y = (5/3)x - (65/3) - (120/3)
y = (5/3)x - (185/3)
Therefore, the equation of the line passing through the point (13,-40) and parallel to the line passing through the points (1,3) and (7,13) in slope-intercept form is:
y = (5/3)x - (185/3)