Question

What is The equation of the line that passes through the points (5,-1) and (4,-5)

Answer 1

For this case we have that by definition, the equation of the line in the slope-intersection form is given by:

$y = mx + b$

Where:

m: It is the slope of the line

b: It is the cut-off point with the y axis

We have two points through which the line passes:

$(x_ {1}, y_ {1}) :( 5, -1)\\(x_ {2}, y_ {2}) :( 4, -5)$

We found the slope:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}} = \frac {-5 - (- 1)} {4-5} = \frac {-5+ 1} {- 1} = \frac {-4} {- 1} = 4$

Thus, the equation is of the form:

$y = 4x + b$

We substitute one of the points and find b:

$(x,y):(5,-1)\\-1=4(5)+b\\-1=20+b\\-1-20=b\\b=-21$

Finally, the equation is:

$y = 4x-21$

Answer:

$y = 4x-21$