Answer:
To write the equation of a line in slope-intercept form, we need two pieces of information: the slope of the line and a point that lies on the line.
Given that the line passes through the point (4, -6) and has a slope of -6, we can use the point-slope form of a line to write the equation. The point-slope form is given by:
y - y₁ = m(x - x₁)
where (x₁, y₁) is a point on the line and m is the slope of the line.
Plugging in the values we have:
y - (-6) = -6(x - 4)
Simplifying the equation, we get:
y + 6 = -6x + 24
To write the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, we need to isolate y on one side of the equation.
Subtracting 6 from both sides, we have:
y = -6x + 18
Therefore, the equation of the line passing through the point (4, -6) with a slope of -6 in slope-intercept form is y = -6x + 18.
Explanation: