Question

Write an equation of the line with the given slope that passes through the given point. m=3/4; (-4, -5)

Answer 1

y +5 = 3 / 4 ( x + 4)

Step-by-step explanation:

The equation of a line in slope-intercept form is given by

`y=mx+b`

where

m = slope

b = y-intercept.

Now we are told that the slope of our line is m = 3/4; therefore, our equation is

`y=(3)/(4)x+b`

Now, what is the value of b?

To find out, we use the fact that the line passes through (-4, -5); therefore, it must satsify x = -4, y = -5. Putting x = -4 and y = -5 into the above equation gives

`-5=(3)/(4)(-4)+b`

Simplifying the above gives

`-5=-(12)/(4)+b`

`\Rightarrow-5=-3+b`

Finally, adding 3 to both sides of the equation gives

`-5+3=b`
`b=-2`

With the value of b in hand, we can now write the equation of the line:

`\boxed{y=(3)/(4)x-2}`

The above equation is our final answer!