Question

What’s the rule for a and b

Answer 1

PART a)

The slope-intercept form of the line equation

$y = mx+b$

where

• m is the slope

• b is the y-intercept

From the figure, let us take two points

• (0, 3)

• (-1, 6)

Finding the slope between (0, 3) and (-1, 6)

(x₁, y₁) = (0, 3)

(x₂, y₂) = (-1, 6)

Using the formula

Slope = m =  [y₂ - y₁] /  [x₂ - x₁]

               =  [6 - 3] / [-1 - 0]

               = 3 / -1  

               = -3

Thus, the slope of the line = m = -3

We know that the value of the 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 b = 3 and m = -3 in slope-intercept form of the line equation

$y = mx+b$

y = -3x+3

Therefore, the rule for the graph 'a' is:

y = -3x+3

PART b)

Given

• The point (0, 10)

• The slope =  rise / run = 4/1

From the graph, it is clear that:

The slope m = [y₂ - y₁] /  [x₂ - x₁]

                     = +4 / +1

                     = 4/1

                     = 4

We know that the value of the 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 = 10

Thus, the y-intercept b = 10

now substituting m = 4 and b = 10 in slope-intercept form of the line equation

$y = mx+b$

y = 4x+10

Therefore, the rule for the graph 'a' is:

y = 4x+10