Question

Find the equation of the line.

Use exact numbers.
100+
y
8+
7+
6+
9 8 7 6 5 4 3 2
2 3 4 5 6 7 8 9
-3
-4
-5
-6+
-7
-8

Answer 1

The equation of the line is:

`y = 3x+3`

The graph is also attached.

Explanation:

The slope-intercept form of the line equation

y = mx+b

where

• m is the slope

• b is the y-intercept

From the straight line on the graph, taking two points

• (0, 3)

• (-1, 0)

Finding the slope between (0, 3) and (-1, 0)

Using the formula

Slope = m = [y₂ - y₁] / [x₂ - x₁]

= [0 - 3] / [-1 - 0]

= -3 / -1

= 3

Thus, the slope of the line = m = 3

We know that the value of y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 3

Thus, the y-intercept b = 3

Now, substituting slope m = 3 and y-intercept b = 3 in the slope-intercept form

y = mx+b

y = 3x+3

Therefore, the equation of the line is:

`y = 3x+3`

The graph is also attached.