Question

Write a linear equation in standard form for the line that goes through (4,4)and (8,3)

Answer 1

The standard equation of a line has the form:

y=mx+b

Where m is the slope of the line and b is the intercept.

The only thing we need to determine the equation of a line is two points, in this case, we have the points (4,4) and (8,3). Then, from the first point we know that when x equals 4 y equals 4 and from the second point we know that when x equals 8 y equals 3, we can express this with the standard formula of a line, like this:

4=m*4+b and 3=8*m+b

subtraction the second expression from the second one, we get:

4-3=m*4+b-8*m-b, we can cancel b and then we have:

4-3=m*4-m*8, we can subtract 3 from 4 in the left side and 8*m from 4*m from the right side and then:

1= -4*m , we can divide both sides by -4 and then:

m= -1/4

Now that we know the value of the slope, we only need to specify the value of b, we can do this by replacing the value of m in the expression 4=m*4+b of the first point and then solve for b, like this;

4=m*4+b, m=-1/4, then:

4= 4*(-1/4)+b, then:

4= -1+b, then, adding -1 in both sides we have:

4+1=b, then:

b=5

And the standar form of the line would be:

y=(-1/4)*x+5