Write an equation of the line that passes through the following two points in standard form: (-1,2), (1,6)

Question

Please I need the answer, because im having trouble

Answer 1

The equation for a line is usually written in the form: y = m*x + b

In this form, m is the slope of the line (rise over run) and b is the y intercept (value of y when x = 0)

 

Since you have two points, we start by calculating the slope (change in y divided by change in x - rise over run).  At the first point, y = 2, and at the second point, y = 6.  So change in y is 6 - 2 = 4.  Now, we calculate the change in x.  At the first point, x = -1, and at the second point, x = 1.  So the change in x is 1 - (-1) = 1 + 1 = 2.  Now, we divide the change in y by the change in x to get the slope.  m = (y₂ - y₁)/(x₂ - x₁) = 4/2 = 2

 

Now that we have the slope, we just need to figure out the y intercept, b.  To do this, plug either of the two given points into the equation for the line and solve for b.  Let's take the first point (-1,2)

 

y = m*x + b

2 = 2*(-1) + b

2 = -2 + b

 

Add 2 to each side of the equation

 

2 + 2 = 2 - 2 + b

4 = 0 + b

4 = b

 

Now we know the slope and we know the y intercept, so we can write out the equation

 

y = 2*x + 4

 

You can plug the second point (1,6) into the equation to double check your answer

 

6 = 2*1 + 4

6 = 2 + 4

6 = 6 (check, everything worked out!)