Question

What is the equation of the line that passes through (0, 3) and (7, 0)?

Answer 1

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

$y = mx + b$

Where:

m: It's the slope

b: It is the cutoff point with the y axis

$m = \frac {y2-y1} {x2-x1}$

According to the data we have two points through which the line passes, then we can find the slope:

$(x1, y1) = (0,3)\\(x2, y2) = (7,0)$

$m = \frac {0-3} {7-0} = - \frac {3} {7}$

Then, the equation is given by:

$y = - \frac {3} {7} x + b$

We substitute a point to find "b":

$3 = - \frac {3} {7} (0) + b\\b = 3$

Finally, the equation is:

$y = - \frac {3} {7} x + 3$

Answer:

$y = - \frac {3} {7} x + 3$