To write the equation of a line in slope-intercept form, we use the formula: y = mx + b, where m represents the slope and b represents the y-intercept.
Given that the line passes through the point (-2, 6) with a slope of -1/4, we can substitute the values into the equation to find the y-intercept.
Let's calculate the y-intercept (b) first. We can use the point-slope formula:
y - y1 = m(x - x1)
Substituting the values (-2, 6) and m = -1/4 into the formula, we have:
y - 6 = (-1/4)(x - (-2))
Simplifying further:
y - 6 = (-1/4)(x + 2)
Next, we can distribute (-1/4) across (x + 2):
y - 6 = (-1/4)x - 1/2
To isolate y, we can add 6 to both sides:
y = (-1/4)x - 1/2 + 6
Simplifying the equation:
y = (-1/4)x + 11/2
Therefore, the equation of the line in slope-intercept form is y = (-1/4)x + 11/2.