how do you Write a point-slope equation for the line with the given slope that contains the given point. with m=-3;(-2,-5)
You use the point slope equation.
I believe it is....
y-y1=m(x-x1)
Solve for y.
y-(-5)=-3(x-(-2))
So y+5=-3x-6
Y=-3x-11
Basically you are now in
Y=mx+b form
To write a point-slope equation for a line, you need two pieces of information: the slope of the line (denoted as 'm') and a point that lies on the line (denoted as (x₁, y₁)). In this case, the slope (m) is given as -3, and the point (x₁, y₁) is (-2, -5).
The point-slope form of a linear equation is:
y - y₁ = m(x - x₁)
Substituting the given slope and point into the equation, you get:
y - (-5) = -3(x - (-2))
Simplifying the equation, you have:
y + 5 = -3(x + 2)
You can further simplify the equation by distributing the -3 on the right side:
y + 5 = -3x - 6
Finally, you can rewrite the equation in standard form by moving all the terms to one side:
3x + y = -11
Therefore, the point-slope equation for the line with slope m = -3 that contains the point (-2, -5) is 3x + y = -11.