Question

Write the equation of the line that passes through the points (8,-2)(8,−2) and (5,5)(5,5). Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.

Answer 1

Answer:

The the equation of the line through the points (8, -2) and (5, 5) in slope-intercept form is

$y=-\frac{7}{3} x+\frac{50}{3}$

Step-by-step explanation:

Let's start by calculation the slope of the line by finding the slope of the segment that joins the two given points (8, -2) and (5,  5):

$slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{5-(-2)}{5-8}\\slope=\frac{7}{-3} \\slope=-\frac{7}{3}$

Now we use this slope in the general slope-intercept form of a line;

$y=mx+b\\y=-\frac{7}{3} x+b$

and then we calculate the value of the intercept "b" by using one of the given points through which the line must pass (for example (5,5) ), and solving for b:

$y=-\frac{7}{3} x+b\\5=-\frac{7}{3} (5)+b\\5=-\frac{35}{3} +b\\b=5+\frac{35}{3}\\b=\frac{50}{3}$

The the equation of the line is

$y=-\frac{7}{3} x+\frac{50}{3}$