What is the slope of the line?

Question

What is the slope?

Graph here:

https://ibb.co/fMrGq0k

Answer 1

The slope of a line is a measure of its steepness or incline and it is calculated as the ratio of the vertical change (the difference in the y-coordinates of two points on the line) to the horizontal change (the difference in the x-coordinates of the same two points). Mathematically, it is often denoted as "m" and is given by the formula:

m=change in y / change in x

For your provided graph let's take 2 points with their coordinates:

point 1 (x1,y1) = (-4, 0) the intersection b/w line and x-axis

point 2 (x2, y2) = (0, -2) the intersection b/w line and y-axis

the slope m should be:

m = (y2-y1) / (x2-x1)

= [(-2)-0] / [0-(-4)]

= (-2)/(+4)

= -1/2

A negative slope indicates a downward incline line.

Answer 2

Hi Shaun,

That graph show two points, incidentally the x and y-intercepts. The x-intercept, where the line crosses the x-axis, is (-4,0). The y-intercept, where it crosses the y-axis, is (0, -2).

Now, for two points, you can compute the slope as:

m= (y₂ - y₁)/(x₂ - x₁), where m=slope, x₁, x₂, y₁, y₂ are x and y-coordinates

x₁= -4

x₂= 0

y₁= 0

y_{2 =} -2

m= (-2-0)/(0--4)

m= -2/4

m= -1/2

I hope this helps.