Question

which equation represents the line passing through points a and c on the graph below?

\\(y = -x - 1\\)
\\(y = -x + 1\\)
\\(y = x - 1\\)
\\(y = x + 1\\)

Explanation:

Identify coordinates of points A and C

Using the Coordinate Transformations knowledge point, we read the coordinates of points \(A\) and \(C\) from the Cartesian plane:
Point \(A\) is located at \((2, 3)\).
Point \(C\) is located at \((-2, -3)\).

Calculate the slope of the line

Using the Slope of a Line knowledge point

$$ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 3}{-2 - 2} = \frac{-6}{-4} = \frac{3}{2} $$

Determine the equation of the line

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK0
$$

Re-evaluating coordinates from the graph

Let's carefully re-examine the grid coordinates of point \(A\) and point \(C\) in the image:

• Point \(A\) is at \(x = 2\), \(y = 3\).
• Point \(C\) is at \(x = -4\), \(y = -3\).

Let's recalculate the slope with \(A(2, 3)\) and \(C(-4, -3)\):
Using the Slope of a Line knowledge point

$$ m = \frac{3 - (-3)}{2 - (-4)} = \frac{6}{6} = 1 $$

Find the correct slope-intercept equation

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Answer:

• \(y = -x - 1\)
• \(y = -x + 1\)
• \(y = x - 1\)
• \(y = x + 1\) (Correct answer)