For this case we have that by definition, the equation of a line in the slope-intersection form is given by:
![y = mx + b](https://img.qammunity.org/2020/formulas/mathematics/high-school/fc4cgm6covys37zv2opmmp9ps4jxyjepvh.png)
Where:
m: It's the slope
b: It is the cutoff point with the y axis
We find the slope with the given points:
![m = \frac {y2-y1} {x2-x1} = \frac {401-450} {14-7} = \frac {-49} {7} = - 7](https://img.qammunity.org/2020/formulas/mathematics/middle-school/1i0nxm0n35cz70m4xzo16cwts7xn9790bs.png)
Thus, the line is given by:
![y = -7x + b](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zkq97x7vc5lnnec77ih13dqytdn993kfzq.png)
We substitute a point to find "b":
![450 = -7 (7) + b\\450 = -49 + b\\450 + 49 = b\\b = 499](https://img.qammunity.org/2020/formulas/mathematics/middle-school/a9o76ya20btsd9tqpg8sn9h41ewohtt8ci.png)
Finally, the equation is:
![y = -7x + 499](https://img.qammunity.org/2020/formulas/mathematics/middle-school/tijdlktdc0d4mq9iofk8gaahh3owefd8oz.png)
Answer:
![y = -7x + 499](https://img.qammunity.org/2020/formulas/mathematics/middle-school/tijdlktdc0d4mq9iofk8gaahh3owefd8oz.png)