Final answer:
The equation of the line with a slope of -1/7 passing through the point (-7, -10) can be written in slope-intercept form as y = -1/7*x + 9.
Step-by-step explanation:
To write the equation of a line with a slope of -1/7 that passes through the point (–7,–10), you can use the point-slope form of the equation of a line which is:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is a point on the line, and m is the slope of the line. Substituting the given point and slope, you get the following equation:
y - (-10) = -1/7(x - (-7))
Simplifying this equation to slope-intercept form (y = mx + b) we get:
y = -1/7*x + (-1/7)*(-7) - 10
Which simplifies to:
y = -1/7*x + 9