Question

Fill in the blanks based on the steps to convert this equation into slope-intercept form: y-3= 5/3 x+6 Step 1: Distributive Property y-3= ____+____ Step 2: Simplify y-3= 5/3 x+______ Step 3: Addition Property of Equality y=5/3x=_____

Answer 1

To convert y-3=5/3x+6 into slope-intercept form, you don't need to use the distributive property or simplify as it's already in simplified form. Add 3 to both sides to solve for y, combining like terms to obtain y=5/3x+9, where the slope is 5/3 and the y-intercept is 9.

Step-by-step explanation:

To convert the equation y - 3 = 5/3x + 6 into slope-intercept form, we need to isolate y on one side of the equation. Here is the step-by-step process:

1. Distributive Property: There is no need to distribute in this equation as there are no parentheses that need to be expanded. So, step 1 would remain y - 3 = 5/3x + 6.
2. Simplify: The equation is already simplified, so step 2 remains the same: y - 3 = 5/3x + 6.
3. Addition Property of Equality: Add 3 to both sides to isolate y: y = 5/3x + 6 + 3.

Combining like terms, we get the slope-intercept form:

y = 5/3x + 9

Where the slope (m) of the line is 5/3 and the y-intercept (b) is 9.

Answer 2

The equation
`y-3 = \((5)/(3)x\) + 6` can be converted to slope-intercept form by applying the Addition Property of Equality, resulting in
`y = \((5)/(3)x\) + 9.`

Step-by-step explanation:

To convert the equation
`y-3 = \((5)/(3)x\) + 6` into slope-intercept form, follow these steps:

1. Apply the Distributive Property: This step does not apply here as there are no parentheses to distribute over. Hence, we skip to the next step.
2. Simplify: No terms on the right-hand side can be combined, so the equation
   `y-3 = \((5)/(3)x\) + 6` is already simplified.
3. Apply the Addition Property of Equality to isolate y: Add 3 to both sides to get
   `y = \((5)/(3)x\) + 9.`

The equation in slope-intercept form is
`y = \((5)/(3)x\) + 9,` where the slope (m) is
`\((5)/(3)\)` and the y-intercept (b) is 9.