What is the point-slope form of the equation for the line with a slope of -2 that passes through the point (4, -6)?
The point-slope form of a linear equation is given by:
y - y1 = m(x - x1)
where m is the slope of the line, and (x1, y1) are the coordinates of a point on the line.
In this case, the slope is -2 and the point is (4, -6). Plugging these values into the formula, we get:
y - (-6) = -2(x - 4)
This simplifies to:
y + 6 = -2x + 8
Rearranging the equation to the standard form, we get:
2x + y = 2
To find the point-slope form of the equation for the line passing through a given point with a given slope, you can use the formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) represents the given point and m represents the given slope.
In this case, the given point is (4, -6), and the given slope is -2. Plugging these values into the formula, we get:
y - (-6) = -2(x - 4)
Simplifying further:
y + 6 = -2x + 8
Therefore, the point-slope form of the equation for the line with a slope of -2 that passes through the point (4, -6) is y + 6 = -2x + 8.
To find the point-slope form of the equation for a line, you need to use the formula:
y - y1 = m(x - x1)
where (x1, y1) is a point on the line and m is the slope.
In this case, the given point is (4, -6), and the slope is -2. Substituting these values into the formula, we have:
y - (-6) = -2(x - 4)
Simplifying, we get:
y + 6 = -2x + 8
Now, we can rearrange the equation to the point-slope form:
y = -2x + 2
So, the point-slope form of the equation for the line with a slope of -2 that passes through the point (4, -6) is y = -2x + 2.