Find the x- and y-intercepts of the line that passes through (-6,-6), (4,-4)

Answer 1

The line that passes through (-6, -6) and (4,-4) has the form y = mx + b

The slope (m) = (y₂ - y₁ )/(x₂ - x₁)

Let (x₁, y₁) = (-6, -6) and let (x₂, y₂) = (4, -4)

Then m = (-4 - (-6)) /(4-(-6)) = 2/10 = 1/5

So, now you have:

y = 1/5(x) + b where b is the y intercept.

So, substituting one of the points into the equation (we'll use (4, -4)):

-4 = 1/5(4) + b

b = -4 - 4/5

b = -4 4/5 or -24/5 (This is the y-intercept that you needed to find)

So, now we can get our final equation of the line passing through these 2 points:

y = (1/5)x - (24/5)

Now , you find the x-intercept by substituting 0 for y in the above equation:

0 = 1/5x - 24/5

(1/5)x = 24/5

x = (24/5)/(1/5) = 24

Therefore, the answer to your problem is:

The x-intercept is the point (24, 0 )

The y-intercept is the point (0,-24/5)

Answer 2

1) Find the slope of the line that passes through these points by using the slope formula. I trust you know that formula. This will give us a slope of 2/10 or 1/5.

2) We now know everything about the formula of the line (y=mx+b) except the value of b. Solve for b by plugging in the x and y values of any known point on the line:

y = mx + b Slope-intercept form

-4 = 1/5 (4) +b Plug in values

-4 = 4/5 + b Simplify

-24/5 = b Subtract 4/5 from both sides and simplify

This gives us the formula y = 1/5 x - 24/5 (Checking your graphing utility will show this to be correct.)

3) The y intercept we can see in the formula (-24/5). To get the x intercept, set y equal to zero, which will give you 24.

Best wishes!

Answer 3

First, you want to find the slope of the line by using the two given points. Slope = difference in y/ difference in x

Slope = 2/10= 1/5. Use the slope and write an equation of the line in point-slope form.

(y-y₁)= m(x-x₁)

y-(-4)= 1/5(x-4)

y+4= 1/5x -4/5

Now that you have a simplified equation, finding the x and y intercepts is easy. Plug in 0 for x and solve for y for the y-intercept. Vice versa for x; plug in 0 for y and solve for x for the x-intercept

Answer 4

The slope m = (-6+4)/(-6-4)=1/5

and (1/5)=(y+4)/(x-4)

This form can be "massaged" into any required form.