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:
[tex] \large \boxed{m = \frac{y_2 - y_1}{x_2 - x_1} }[/tex]
m-term represents the slope from y = mx+b.
We are given two coordinate points. Substitute the points in the formula.
[tex] \large{m = \frac{7 - 5}{3 - 0} } \\ \large{m = \frac{2}{3} }[/tex]
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:
[tex] \large{y = \frac{2}{3} x + b}[/tex]
Then choose one of two points to substitute. I will choose (0,5). Therefore substitute x = 0 and y = 5.
[tex] \large{5 = \frac{2}{3} (0) + b} \\ \large{5 = 0 + b} \\ \large{b = 5}[/tex]
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.
[tex] \large{y = \frac{2}{3} x + 5}[/tex]
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.
