What is an equation of the line that passes through the points (-5, -8) and (5,4)?

Question

i need to find b

Answer 1

Hi, Zuri!

One way that we can write the equation of a line that passes through these points is by using slope-intercept form: y = mx + b, where m is the slope of the line and b is the y coordinate of the y-intercept. We are not directly given m or b, but we can use the two points that we are given to solve for them.

We can start by solving for m. The slope of a line is equal to the change in y over the change in x (or the "rise over run"). This can be expressed by the formula:

m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are any two points on the line.

For this problem, let's assign (-5, -8) = (x₁, y₁) and (5, 4) = (x₂, y₂) (you could also do this in the reverse order, it doesn't necessarily matter which point is which so long as everything stays consistent throughout the problem). This allows us to solve for m:

m = (4 - (-8)) / (5 - (-5))

m = (4 + 8) / (5 + 5)

m = 12/10

m = 6/5

We can then plug this value of m into our formula for a line to get y = (6/5)x + b. Next, we need to solve for b. In order to do this, we can select either point and plug it into the formula above. I will choose (5, 4), but you either one should give the same answer. Plugging this point into the formula yields:

4 = (6/5)(5) + b

4 = 6 + b

b = -2

Thus, we have our values of m and b, and can plug them into our general form to write the equation of a line that passes through our given points:

y = (6/5)x + (-2) --> y = (6/5)x - 2

I hope that this explanation was helpful, and please don't hesitate to reach out if you have any further questions!

Answer 2

Slope is Δy/Δx, or [4 - (-8)]/[5 - (-5)] = 12/10 = 6/5

Using one of the two points in y = mx + b yields 4 = 5(6/5) + b → 4 = 6 + b

So b must be -2. The final equation is y = (6/5)x - 2

Answer 3

First you need to find the slope of the line passing through those points.

m = (4-(-8))/ (5-(-5))= 12/10=6/5

Now you can choose either point (I choose (5,4)) and apply it to y=mx + b (finding b) or to point-slope y-y₁=m(x-x₁).

Applying to y = mx + b.

4 = (6/5)5 + b (notice that 5 was substituted for x and 4 for y.

b = -2

So the equation is: y = (6/5)x - 2

Using point-slope:

y - 4 = 6/5 (x-5) (this time 4 substituted for y₁ and 5 for x₁)

y - 4 = (6/5)x - 6

y = (6/5)x - 2