Write in point-slope form an equation of the line through the pair of points. (11, 1) and (5, 8)
What is an equation of the line in point-slope form?
a.) y - 1 = 7/6 (x - 11)
b.) x - 1 = -7/6 (y - 11)
c.) y = 7/6x + 83/6
d.)y - 1 = -7/6 (x - 11)
I have to show my work as well, idk how to do this
slope = (8-1) / (5-11) = 7/-6 = -7/6
so
y = 1 -(7/6)(x-11)
or
y-1 = -7/6(x-11)
That starts at x = 11, y = 1 and marches down with a slope of -7/6
To find the equation of a line in point-slope form, we need two pieces of information: one point on the line and the slope of the line.
Given the pair of points (11, 1) and (5, 8), we can calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Substituting the values of the two points into the formula, we get:
slope = (8 - 1) / (5 - 11) = 7 / -6 = -7/6
Now that we have the slope, we can use it along with one of the points to write the equation of the line in point-slope form:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) are the coordinates of one of the points.
Substituting the values x1 = 11, y1 = 1, and m = -7/6 into the equation, we get:
y - 1 = -7/6(x - 11)
So, the correct answer is:
d.) y - 1 = -7/6(x - 11)