Final Answer:
A line has a slope of –5/6 and passes through the point (–6, –1) is y = (-5/6)x - 6.
Step-by-step explanation:
To write the equation of a line in slope-intercept form (y = mx + b), you need the slope (m) and the y-intercept (b). Here, we are given the slope of the line, m = -5/6, and a point through which the line passes, which is (-6, -1).
We can use the point-slope form of the equation of a line to find the equation that contains the given point. The point-slope form is:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line (in this case, (-6, -1)) and m is the slope of the line.
Let's plug in the values:
y - (-1) = (-5/6)(x - (-6))
y + 1 = (-5/6)(x + 6)
Now we simplify the equation and solve for y to get it into slope-intercept form:
y + 1 = (-5/6)x - (5/6)(6)
y + 1 = (-5/6)x - 5
y = (-5/6)x - 5 - 1
y = (-5/6)x - 6
Now we have the equation of the line in slope-intercept form:
y = (-5/6)x - 6
This is the final equation, with the slope -5/6 and the y-intercept -6.