How do I determine the equasion of the line with a slope of -3 which contains the point (-7,2)?

Question

Would the following format work: Y=M(X-Px)+Py?  What does the point (-7,2) mean?

Answer 1

Jessie,

 

The equation for a line which passes through a specified point and where the slope is given is:

 

(y - y₁₎ = m·(x - x₁)

 

the point (-7,2) is given in (x,y) form and lies on the graph at the position x = -7, y = +2

 

Since you're give that the slope m = -3, we just need to plug in the numbers:

 

(y - 2) = -3·(x + 7)

 

We can simplify this a bit by combining and rearranging:

 

y = -3·x - 21 +2

 

y = -3·x - 19

Answer 2

The equation of a straight line is y = mx + b, where m is the slope and b is the y-intercept.  To find the equation of a particular line, we need find the values of m and b.  The problem gives you the slope, so we know m = -3.  The equation becomes:

 

y = -3x + b

 

Now we just need to find b to have the whole equation.  To do that, plug in the point (-7,2).  This is known an ordered pair in the format (x,y),  It specifies the x and y coordinates of a point on a graph.  It is called an ordered pair because the x-value always appears first and the y-value of the point appears second.  So (-7,2) represents a single point on the line with x=-7 and y = 2.  Let's plug those x,y values into our equation to find b:

 

2 = (-3)(-7) + b

 

2 = 21 + b

 

-19 = b

 

So the equation is:

 

y = -3x - 19

Answer 3

You would determine the equation using the point slope formula which is (y-y₁)=m(x-x₁) 

 

y1 would be the 2 because that is the point you are given 

x₁ would be the -7 it is also given 

m is your slope which is -3 

 

now plug in 

 

(y-2)=-3(x-(-7)) 

y-2= -3x -21 

y=-3x-19