Question

what equation in slope intercept form represents the line that passes through the (-1, 10) and (5,8)?

Answer 1

You are given two points, (-1, 10) and (5, 8). You are required to find the equation in slope intercept form given the points. The equation of a slope intercept form is y = mx + b. Where m is the slope and b is the y-intercept. By definition, slope, m, is the rise over run or the difference of y over the difference of x.  

m = y2-y1/x2-x1
Let us denote y2=8, y1=10, x2=5 and x1=-1 and we get
m = 8-10/5-(-1)
m = -1/3, a negative slope means it is rising to the left of the graph.  

Since the slope passes the two points, it also passes the y-intercept. Choose one of the points, (-1, 10) and substitute it to y = mx + b.  

y = mx + b
10 = (-1/3)(-1) + b
b = 29/3  
The equation now is y = -1/3x + 29/3.