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Question

A coordinate plane's x-axis ranges from negative 4 to 4 and its y-axis ranges from negative 6 to 8, both in unit increments. A line is plotted sloping down and to the right. It intercepts the y-axis at left parenthesis 0 comma 2 right parenthesis.

Which option gives the point-slope form of the equation of the graphed line?

(1 point)
Responses

y=1/2x−2.5
y equals Start Fraction 1 over 2 End Fraction x minus 2.5

y+4=1/2(x−3)
y plus 4 equals Start Fraction 1 over 2 End Fraction left parenthesis x minus 3 right parenthesis

y+2=1/2(x−1)
y plus 2 equals Start Fraction 1 over 2 End Fraction left parenthesis x minus 1 right parenthesis

x−2y=5

Answer 1

To find the point-slope form of the equation of the line that intercepts the y-axis at (0, 2) and slopes down to the right, we need to identify the slope of the line first.

A line that slopes down to the right has a negative slope. Given the intercept at (0, 2), we can determine the slope by identifying another point or by examining the options.

1. Intercept and slope: The line passes through (0, 2). Let's consider the first option provided and determine if its slope agrees with the intercept and the direction of the line. The answer choices are of the form \( y - y_1 = m(x - x_1) \).

2. Finding the slope:

   • From the given options, we note options use a positive slope \( \frac{1}{2} \).
   • However, since the question mentions that the line slopes down to the right, we expect the slope to be negative.
   • The points suggested in any option mainly differ only in starting intercepts.

3. Validating forms:

   • The first option shows a positive slope, meaning it cannot represent a line with a downward slope.

4. Finding valid candidates:

   • The second option, \( y + 4 = \frac{1}{2}(x - 3) \), implies iteration on levels 4 units above \( (0, 2) \).
   • The third option, \( y + 2 = \frac{1}{2}(x - 1) \), also suggests upward movement from \( (0, 2) \).

Since all the slopes are not negative, it makes it clear that none of the options are correctly representing a line that would slope down to the right with a positive slope.

Thus, we can determine no valid option exists that represents the line in question as described.

Given that, if forced to choose, none of the options work for the described line through the intercept (0,2) while maintaining a downward slope.

However, if confirming the form only, while retaining the negative principle in slope validation, we could summarize:

• Correct slope of line: \( m < 0 \).
• Correct equation format: \( y - 2 = m(x - 0) \).

Given all above, the following valid choice remains:

None of the given statements satisfy the request for the correctly plotted line representation within point-slope expectations.

Please confirm if further adjustments on testing options are required or any specific segments needed.

Answer 2

just pick a answer

Answer 3

Given the provided options and knowing that the line slopes down to the right, the best option to select from the available answers would be:

y + 2 = 1/2(x - 1)

This option follows the point-slope form and utilizes a point likely on or near the line, despite incorrect slope expectation based on prior deductions.

Please note that it doesn't match the characteristic of a downward slope but is the least incorrect choice from the alternatives presented.