The x intercept of a line is -5 and the y intercept of the line i’d -2.what is the equation of the line?

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

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.