Answer:
The equation of the line in slope-intercept form is:
[tex]y=-\frac{3}{7} x+3\\[/tex]
In one of the many possible standard forms:
[tex]3\,x+7\,y=21[/tex]
Step-by-step explanation:
First calculate the slope of the segment that joins these two points: (0, 3) and (7,0):
[tex]slope=\frac{y_2-y_1}{x_2-x_1}= \frac{0-3}{7-0}=-\frac{3}{7}[/tex]
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:
[tex]y=m\,x+b\\y=-\frac{3}{7} x+3[/tex]
And now, if you want to write the equation eliminating fractions, we can multiply both sides by "7":
[tex]y=-\frac{3}{7} x+3\\7\,y=-3\,x+21\\3\,x+7\,y=21[/tex]