Question

IWhat is the equation of a line that passes through the points (3, 6) and (8, 4)?

Answer 1

Answer:

$(x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)$

$m =\frac{y_2 -y_1}{x_2 -x_1}$

And replacing we got:

$m=\frac{4-6}{8-3}= -\frac{2}{5}$

And for this case we can use the first point to find the intercept like this:

$6 = -\frac{2}{5}(3) +b$

And solving we got:

$b = 6 +\frac{6}{5}= \frac{36}{5}$

And then the line equation would be given by:

$y = -\frac{2}{5}x +\frac{36}{5}$

Step-by-step explanation:

For this case we have the following two points given:

$(x_1 =2, y_1 = 6), (x_2 = 2, y_2 = 4)$

And for this case we want an equation for a line with the two points given by:

$y = mx+b$

Wher m is the slope and b the y intercept. We can find the slope with this formula:

$m =\frac{y_2 -y_1}{x_2 -x_1}$

And replacing we got:

$m=\frac{4-6}{8-3}= -\frac{2}{5}$

And for this case we can use the first point to find the intercept like this:

$6 = -\frac{2}{5}(3) +b$

And solving we got:

$b = 6 +\frac{6}{5}= \frac{36}{5}$

And then the line equation would be given by:

$y = -\frac{2}{5}x +\frac{36}{5}$