What is the equation of the line shown in this graph?

Solution:

The equation of a line is an algebraic form of representing the set of points, which together make up a line in a coordinate system. We have different forms of an equation of a line.

We know that the general equation of a straight line is given by y = mx + c

Here,

m = Slope of the line

c = y-intercept of the line

Given two points on a straight line (x₁, y₁) and (x₂, y₂) the slope is calculated by using the slope formula m = (y₂ - y₁) / (x₂ - x₁) ------ (1)

Let's look into the graph shown below

From the graph we see that, the coordinates (x₁, y₁) and (x₂, y₂) are A (-6,0) and B (0,-3), respectively.

Let's calculate the slope 'm' using equation (1).

m = (-3 - 0) / (0 - (-6))

m = -3 / 6 = -1 / 2

You can use Cuemath's online slope calculator to find the slope.

Also, we see that the line cuts the y-axis at y = -3

Thus, the y-intercept is c = -3

Substituting the values of 'm' and 'c' in y = mx + c we get,

y = (-1/2)x - 3

Thus, the equation of the line shown in this graph is y = (-1/2)x - 3.

What is the equation of the line shown in this graph?

Summary:

The equation of the line shown in this graph is y = (-1/2)x - 3