Question

A coordinate grid with a line passing through the points (negative 2, negative 1) and (2, 0) Use the graph of the line to answer the questions. What is an equation of the line in point-slope form? How can the point-slope form be written in function notation?

Answer 1

1. What is an equation of the line in point-slope form?

y+1=[1/3][x+2]

2.How can the point-slope form be written in function notation?

f[x]=[1/3]x-[1/3]

Answer 2

The general equation for a line (written in the slope-intersect form) is:

y = f(x) = a*x + b

Such that the line is already written in function notation.

Where a is the slope, and b is the y-intersect.

If a line passes through a point (x₁, y₁) and (x₂, y₂), the slope can be written as:

y = (y₂ - y₁)/(x₂ - x₁)

We know that the line in the graph passes through the points:

(-2, -1) and (2, 0)

Then the slope of the line will be:

a = (0 - (-1))/(2 - (-2)) = 1/4

Then the function for the line will be something like:

y = f(x) = (1/4)*x + b

Now we want to find the value of b.

Because we know that this function passes through the point (2, 0), this means that:

f(2) = 0 = (1/4)*2 + b

We can solve that for b:

0 = 2/4 + b

-2/4 = b

Then the function for the line is:

y = f(x) = (1/4)*x - 2/4