What is the slope of a line that passes through (-2, -3) and (1, 1)?

1 Answer
Nov 10, 2015

Use the two coordinates formula to figure out the equation of a straight line.

Explanation:

I do not know if by slope you mean the equation of the line or simply the gradient.

Gradient Only Method

To get the gradient you simply do dy/dx which means difference in y over difference in x

The formula expanded means we do (y_2-y_1)/(x_2-x_1) where our coordinates are (x_1,y_1) and (x_2,y_2)

For your example we substitue the values in to get (1-(-3))/(1-(-2))

This turns into (1+3)/(1+2) simplified this is 4/3 so your gradient or 'slope' is 4/3 or 1.dot 3

Equation of Straight Line Method

As for the full equation we use the two coordinates formula.

This formula is: (y-y_1)/(y_2-y_1) = (x-x_1)/(x_2-x_1) where our coordinates are (x_1,y_1) and (x_2,y_2).

If we substitute in your values we get: (y-(-3))/(1-(-3)) = (x-(-2))/(1-(-2))

Tidying up the negatives we get: (y+3)/(1+3) = (x+2)/(1+2)

Simplifying we get: (y+3)/4 = (x+2)/3

Now we must rearrange this expression into the form y=mx+c

To do this we will first multiply both sides by 4 to remove the fraction. If we do this we get: y+3 = (4x+8)/3

Then we will multiply both sides by 3 to remove the other fraction. This gives us: 3y+9 = 4x+8

Take away 9 from both sides to get y on its own: 3y = 4x-1

Then divide by 3: y = 4/3x - 1/3

In this case you can also get the gradient as the m part of the equation: y=mx+c is the gradient. Which means that the gradient is 4/3 or 1.dot 3 as we got using the first method.

Interestingly we can also use the c part of the equation to figure out the y intercept. In this case it is 1/3 which means the y intercept of this line is at the coordinate (1/3,0)