Hey!
There are two ways to solve this problem, I have showed you both of them below:
Method 1 -:
So we know that the x-intercept of the line is at (-5,0) and the y-intercept is at (0,-2). The most common form of the equation of a line is the slope-intercept form which is written as y=mx+b. In this equation, y and x are two points on the line, m is the slope and b is the y-intercept.
We are given the value of b which is -2. We also know two points on the line so we can find the slope. The formula for slope is (y2-y1)/(x2-x1). We can now plug in the points into the equation and get (0-(-2)/(-5-0). This simplifies to -2/5. That is your slope.
Now that we know this, we have solved for everything we need for writing the equation of the line. The equation of the line is:
y = (-2/5)x - 2
Method 2 -:
This method is a bit easier but will still give you the same result. Since you already know the y-intercept as -2, you know the value of b. You also have atleast one point so you can just plug it into the equation y = mx + b.
Now you can just plug in a point for x and y. We also know the x-intercept and that might be easier to use for solving. The x-intercept is (-5,0) and we can plug this into the equation to get 0 = m(-5) + (-2). We can now rewrite this as 0 = -5m - 2.
The next thing we do is solve for x:
0 = -5m - 2
2 = -5m
-2/5 = m
Now we know that m = -2/5, we can put this into the equation along with the y-intercept to get our answer.
y = (-2/5)x - 2