Question

6. X y -3 # 12 18 a) y = 1/3x + 6 c) y = 2x+6 036 06 Given the table, write the equation in the slope- intercept form. b) y = 3x + 6 d) y = 1/2x + 6​

Answer 1

The equation in slope-intercept form is
`\(y = (8)/(7)x + 15\).`


Let's determine the equation in slope-intercept form step by step.

We want to find the equation in the form
`\(y = mx + b\)`, where m is the slope and b is the y-intercept.

Step 1: Calculate the Slope (\(m\))

`\[ m = \frac{\text{Change in } Y}{\text{Change in } X} \]\[ m = (36 - 12)/(18 - (-3)) \]\[ m = (24)/(21) \]\[ m = (8)/(7) \]`

So, the slope m is
`\( (8)/(7) \)`.

Step 2: Use the Slope-Intercept Form \(y = mx + b\) and substitute the slope:

`\[ y = (8)/(7)x + b \]`

Now, we need to find the y-intercept (\(b\)). We can use one of the given points (let's use (-3, 12)) to solve for \(b\).

`\[ 12 = (8)/(7) \cdot (-3) + b \]`

Now, solve for b:

`\[ 12 = -(24)/(7) + b \]`

To simplify, multiply both sides by 7 to get rid of the fraction:

`\[ 84 = -24 + 7b \]`

Add 24 to both sides:

`\[ 7b = 108 \]`

Divide by 7:

`\[ b = 15 \]`

So, the y-intercept b is 15.

Step 3: Substitute the slope and y-intercept back into the equation:

`\[ y = (8)/(7)x + 15 \]`

Therefore, the equation in slope-intercept form is
`\(y = (8)/(7)x + 15\).`