Ask a New Question
Menu

What is the slope-intercept form of the equation of the line parallel to the line in the graph that passes through the point (3,3)?

(1 point)
Responses

y=−32x+112
y is equal to negative 3 halves x plus 11 halves

y=23x+1
y is equal to 2 thirds x plus 1

y=−32x+152
y is equal to negative 3 halves x plus 15 halves

y=23x−1

1 answer

To determine the slope-intercept form of a line that is parallel to a given line and passes through a specific point, we need to follow these steps:

  1. Identify the slope of the given line: If the slope of the original line is \( m \), then the slope of any line parallel to it will also be \( m \).

  2. Use the point-slope form of a linear equation to find the equation of the line that passes through the given point.

  3. Convert this equation to slope-intercept form if necessary.

Without the graph provided, we cannot definitively determine the slope of the original line. However, we can examine the options you've provided to extract the slopes and see which are candidates for being parallel lines:

  • \( y = -\frac{3}{2}x + \frac{11}{2} \) (slope = \(-\frac{3}{2}\))
  • \( y = \frac{2}{3}x + 1 \) (slope = \(\frac{2}{3}\))
  • \( y = -\frac{3}{2}x + \frac{15}{2} \) (slope = \(-\frac{3}{2}\))
  • \( y = \frac{2}{3}x - 1 \) (slope = \(\frac{2}{3}\))

Next, let's determine which of these lines can be formed through the point (3, 3) using the slopes:

If the slope is \(-\frac{3}{2}\) (from the first and third options), using the point-slope form, we do:

\[ y - 3 = -\frac{3}{2}(x - 3) \] \[ y - 3 = -\frac{3}{2}x + \frac{9}{2} \] \[ y = -\frac{3}{2}x + \frac{9}{2} + \frac{6}{2} \] \[ y = -\frac{3}{2}x + \frac{15}{2} \]

This matches the third option \(y = -\frac{3}{2}x + \frac{15}{2}\).

Now, if the slope is \(\frac{2}{3}\) (from the second and fourth options), we do similarly:

\[ y - 3 = \frac{2}{3}(x - 3) \] \[ y - 3 = \frac{2}{3}x - 2 \] \[ y = \frac{2}{3}x + 1 \]

This matches the second option \(y = \frac{2}{3}x + 1\).

Conclusion:

From this analysis, the lines that are parallel to the original line and pass through the point (3, 3) could be:

  • \(y = -\frac{3}{2}x + \frac{15}{2}\) (Option 3)
  • \(y = \frac{2}{3}x + 1\) (Option 2)

Without knowing the original slope, we conclude that both options are valid depending on the slope in the graph. If you see the line's slope on the graph is \( -\frac{3}{2} \), then the answer is:

\(y = -\frac{3}{2}x + \frac{15}{2}\) If the slope is \( \frac{2}{3} \), then the answer is:

\(y = \frac{2}{3}x + 1\)

Choose based on the graph visible to you!