Question

How do I write an equation in point- slope form based on this graph?

Answer 1

Point-Slope Form of a Line

The equation of a line can be written in the so-called point-slope form as:

y = m(x - h) + k

Where m is the slope of the line and (h,k) is a point through which the line passes.

We need to determine the values of m, h, and k from the graph.

It can be seen the point (-3,1) belongs to the line, thus h = -3, k=1

To find the slope we need a second point. Though it's not directly given, we can take it from the graph. A clear point through which the line passes is (-2,-2).

The slope of a line can be calculated with the formula:

`m=(y_2-y_1)/(x_2-x_1)`

The coordinates of the points are (-3,1) and (-2,-2), thus:

`m=(-2-1)/(-2+3)=(-3)/(1)=-3`

We now have the data needed to express the equation of the line:

y = -3 (x + 3) +1

It can also be expressed as:

y - 1 = -3( x + 3)