Question

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

Answer 1

Answer:

The equation of the line in slope-intercept form is:

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

In one of the many possible standard forms:

$3\,x+7\,y=21$

Step-by-step explanation:

First calculate the slope of the segment that joins these two points: (0, 3) and (7,0):

$slope=\frac{y_2-y_1}{x_2-x_1}= \frac{0-3}{7-0}=-\frac{3}{7}$

Now, knowing that the y-intercept is (0, 3) [point on the y-axis (for x=0) where the line crosses], Then the equation of the line in slope-intercept form is:

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

And now, if you want to write the equation eliminating fractions, we can multiply both sides by "7":

$y=-\frac{3}{7} x+3\\7\,y=-3\,x+21\\3\,x+7\,y=21$