To find an equation of a line, you have to know the value of slope first. We can find the value of slope by using the formula below:
![\large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }](https://tex.z-dn.net/?f=%20%5Clarge%20%5Cboxed%7Bm%20%3D%20%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D%20%7D)
m-term represents the slope from y = mx+b.
We are given two coordinate points. Substitute the points in the formula.
![\large{m = \frac{7 - 5}{3 - 0} } \\ \large{m = \frac{2}{3} }](https://tex.z-dn.net/?f=%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B7%20-%205%7D%7B3%20-%200%7D%20%7D%20%5C%5C%20%20%5Clarge%7Bm%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%7D)
Therefore the slope is 2/3.
Next we find the y-intercept. In the form of y = mx+b where m = slope and b = y-intercept. We have got slope, except the y-intercept. We can find the y-intercept by substituting one of gjven points in the equation of y = mx+b.
Since we know the slope - we can rewrite the equation like below:
![\large{y = \frac{2}{3} x + b}](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20x%20%2B%20b%7D)
Then choose one of two points to substitute. I will choose (0,5). Therefore substitute x = 0 and y = 5.
![\large{5 = \frac{2}{3} (0) + b} \\ \large{5 = 0 + b} \\ \large{b = 5}](https://tex.z-dn.net/?f=%20%5Clarge%7B5%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20%280%29%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7B5%20%3D%200%20%2B%20b%7D%20%5C%5C%20%20%5Clarge%7Bb%20%3D%205%7D)
Thus the y-intercept is (0,5). Note that if the question gives you (0,a) point. That is the y-intercept of graph. So b = a if given (0,a).
Rewrite the equation by substituting the b-value.
![\large{y = \frac{2}{3} x + 5}](https://tex.z-dn.net/?f=%20%5Clarge%7By%20%3D%20%20%5Cfrac%7B2%7D%7B3%7D%20x%20%2B%205%7D)
Hence, the equation of a line that contains those points is y = 2x/3 + 5
Answer
Hope this helps! Let me know if you have any doubts.