Using the provided graph, write the equation of the line in slope-intercept form, standard form, and point-slope form. The points (-2, 3) and (2, 1) lie on the line. a. Slope-intercept form: \( y = mx + b \) b. Standard form: \( ax + by = c \) c. Point-slope form: \( y - y_1 = m(x - x_1) \)

 Let's find the equation of the line that passes through the points (-2, 3) and (2, 1).

First, we calculate the slope (m) of the line using the formula: m = (change in y) / (change in x) = (y2 - y1) / (x2 - x1)

Plugging in our points (-2, 3) as (x1, y1) and (2, 1) as (x2, y2), we get: m = (1 - 3) / (2 - (-2)) = (-2) / (4) = -1/2

a. Slope-intercept form (y = mx + b): Now we need to find the y-intercept (b). We can use either of the points for this. Let's use the point (-2, 3). 3 = (-1/2)(-2) + b 3 = 1 + b b = 2

Therefore, the equation in slope-intercept form is: y = -1/2x + 2

b. Standard Form (ax + by = c): To convert the slope-intercept form to standard form, we rearrange the terms: y = -1/2x + 2

Multiply everything by 2 to eliminate the fraction: 2y = -x + 4 Rewrite it: x + 2y = 4

Here, we have the standard form, where a = 1, b = 2, and c = 4.

c. Point-Slope Form (y – y1 = m(x – x1)): We can use either point. Using (-2, 3) and our slope m = -1/2, the equation will be: y – 3 = -1/2(x – (-2)) y – 3 = -1/2(x + 2)

That is the point-slope form of the equation.