The equation of the line passing through the points (-1,6) and (3,-2) in slope-intercept form is y = -2x + 4.
By using the graph we can identify the two points are (-1,6) and (3,-2)
To write the equation of a line in slope-intercept form, we need two pieces of information: the slope of the line and the y-intercept.
The points (-1,6) and (3,-2), we can find the slope using the formula:
slope = (change in y) / (change in x)
Substituting the coordinates of the two points:
slope = (-2 - 6) / (3 - (-1))
= -8 / 4
= -2
Now that we have the slope, we can use the point-slope form of the equation:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
Using the point (-1,6) and the slope -2:
y - 6 = -2(x - (-1))
y - 6 = -2(x + 1)
y - 6 = -2x - 2
y = -2x + 4
Therefore, the equation of the line passing through the points (-1,6) and (3,-2) in slope-intercept form is y = -2x + 4.