Find the slope and y-intercept of the line through the points (-3,-4) and (0,-1)

The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept.

The slope m of this line can be calculated like this:

                                           m = change in y-value /   change in x-value

we are given (x₁,y₁) as (-3,-4) and (x₂,y₂) as (0,-1)

so slope m is:

m = (y₂ - y₁) / (x₂ -x₁)

    = -1 - (-4) / 0 -(-3)

    = 3 / 3

     = 1

You can find the y-intercept by looking at the graph and seeing which point crosses the y axis. This point will always have an x coordinate of zero.

Now,

y = x + b (since the value of m has been calculated as 1 as shown above)

⇒ b = y - x            

⇒b = -4 - (-3)    [if we put in the values from our first point (-3, -4)]

⇒b = -1 is the y intercept

Note:

if we put in the values from our second point (0, -1) in b = y - x, then also we get b = -1 as the y intercept