Question

Write the equation in point slope form 4,1 -2,7

Answer 1

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

$y = mx + b$

Where:

m: It's the slope

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

The slope can be found using the formula:

$m = \frac {y_ {2} -y_ {1}} {x_ {2} -x_ {1}}$

We have the following points:

$(x_ {1}, y_ {1}): (-2,7)\\(x_ {2}, y_ {2}): (4,1)$

Thus, the slope is:

$m = \frac {1-7} {4 - (- 2)} = \frac {-6} {4 + 2} = \frac {-6} {6} = - 1$

Thus, the equation is of the form:

$y = -x + b$

We substitute a point and find "b":

$1 = -4 + b\\1 + 4 = b\\b = 5$

Finally, the equation is:

$y = -x + 5$

Answer:

$y = -x + 5$