Question

I need help asap plz

Answer 1

y=-2/3x+3

Explanation:

Linear equations most commonly take place in slope-intercept form:

y=mx+b

Here's what the variables mean:

y=the y-coordinate

m=the slope

x=the x-coordinate

b=the y-intercept (the point on the line that crosses the y-axis)

In a linear equation, y and x are left as y and x when m and b are replaced with numbers.

1. Calculate the Slope (m)

We can do this by using the formula
`(y_2-y_1)/(x_2-x_1)`. We plug in any two given points:
`(x_1, y_1)` and
`(x_2,y_2)`.

Because it's easier to calculate with non-fractional values, we can pick the last two points: (3,1) and (6,-1).

`(y_2-y_1)/(x_2-x_1)\\\\(-1-1)/(6-3)\\= (-2)/(3)`

Therefore, the slope of the line (m) is equal to -2/3.

So far, our equation looks like this: y=-2/3x+b.

2. Calculate the y-intercept (b)

To find the y-intercept, we take our equation y=-2/3x+b, plug in any point and solve for b. Let's use the point (3,1).

`y=-(2)/(3)x+b\\1=-(2)/(3)(3)+b\\`

3 cancels out

`1=-2+b\\`

Add 2 to both sides to isolate b

`1=-2+b\\1+2=-2+b+2\\3=b`

Therefore, the y-intercept (b) is equal to 3.

Now, our equation looks like this: y=-2/3x+3.

I hope this helps!