Answer:
The the equation of the line through the points (8, -2) and (5, 5) in slope-intercept form is
[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]
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):
[tex]slope=\frac{y_2-y_1}{x_2-x_1} \\slope=\frac{5-(-2)}{5-8}\\slope=\frac{7}{-3} \\slope=-\frac{7}{3}[/tex]
Now we use this slope in the general slope-intercept form of a line;
[tex]y=mx+b\\y=-\frac{7}{3} x+b[/tex]
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:
[tex]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}[/tex]
The the equation of the line is
[tex]y=-\frac{7}{3} x+\frac{50}{3}[/tex]
