Write a slope-intercept equation for a line with the given characteristics:

m = 2/3 passes through (-4,-5)

I got an answer but would like to compare to see what someone else gets. Thanks!

y=mx+b

put in x,y, and m, then solve for b.

I came up with 7 2/3 is this correct, and if so do i need to turn it into an improper fraction? Thanks

subbing into bob's equation...

-5 = (2/3)(-4) + b
-15 = -8 + 3b
b = -7/3

so your equation is
y = (2/3)x - 7/3

How can this be? I got -8/3 because I multiplyed 2/3 and -4..Is this correct?

I usually clear my fractions, in this case I multiplied each term by 3

ok, your way...
-5 = (2/3)(-4) + b
-5 = -8/3 + b
-5 + 8/3 = b
-15/3 + 8/3 = b
-7/3 = b

see how much more complicated it gets if you keep the fractions ?

Thank you, I see how complicated it is when keeping the fractions. It makes sense now, thanks!

To write a slope-intercept equation for a line, we need to use the formula: y = mx + b, where m is the slope and b is the y-intercept.

Given that the slope (m) is 2/3, we can substitute this value into the equation: y = (2/3)x + b.

We also know that the line passes through the point (-4,-5). To find the y-intercept (b), we can substitute the x and y coordinates of the given point into the equation and solve for b.

Using the point (-4,-5), we have: -5 = (2/3)(-4) + b.

Now let's solve for b:

-5 = (-8/3) + b
Multiply each term by 3 to get rid of the fraction:
-15 = -8 + 3b
Add 8 to both sides:
-7 = 3b
Divide both sides by 3:
b = -7/3

So the value of b is -7/3.

Now we can write the slope-intercept equation for the line with the given characteristics:

y = (2/3)x - 7/3

Thus, the slope-intercept equation for the line is y = (2/3)x - 7/3.

You can compare your answer to this solution to check if you got the same equation.