Question

Which of the following equations describes the line shown below? Check all that apply.

A. \(y-12 = \frac{1}{4}(x-6)\)

B. \(y-6 = 4(x-12)\)

C. \(y-4 = 4(x-4)\)

D. \(y-6 = \frac{1}{4}(x-12)\)

E. \(y-4 = \frac{1}{4}(x-4)\)

F. \(y-12= 4(x-6)\)

Answer 1

To identify which equations describe the line, we need to rewrite the point-slope form equations to slope-intercept form and compare them to the characteristics of the described line, paying particular attention to the slope and y-intercept.

Step-by-step explanation:

The equation that describes a linear equation is typically in the form y = mx + b, where m is the slope and b is the y-intercept. To determine which given equations describe the line, we need to consider both the slope and the y-intercept that the line would have based on the equation.

With the slope-intercept form in mind, we can transform the given point-slope equations to slope-intercept form to see if they match the slope and y-intercept of the line in question. For example, we can rearrange equation A like this:

1. Add 12 to both sides: y = ⅓(x - 6) + 12
2. Distribute the ⅓ and simplify: y = ⅓x - ⅓⋅6 + 12
3. Combine like terms to get the slope-intercept form: y = ⅓x + some number

By comparing equations A through F to the described line, we check for a consistent slope and y-intercept with the line in question. We would then select any of the equations that have a slope of 4 if the line rises 4 units with each unit increase in x (positive slope), or a slope of ⅔ if the line rises 1 unit for every 4 units increase in x (positive slope).