a line passes through the point (-4,6) and has a slope of -5/4. Write an equation in point-slope form for this line.
To write the equation of a line in point-slope form, we need the coordinates of a point on the line and the slope of the line. In this case, we are given the point (-4,6) and a slope of -5/4.
The point-slope form of a line is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope.
Substituting the given values into the formula, we have:
y - 6 = (-5/4)(x - (-4))
Simplifying the equation, we have:
y - 6 = (-5/4)(x + 4)
Therefore, the equation in point-slope form for the line passing through the point (-4,6) with a slope of -5/4 is y - 6 = (-5/4)(x + 4).
To write an equation in point-slope form, we will use the formula:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Given that the point is (-4, 6) and the slope is -5/4, we can substitute these values into the formula:
y - 6 = -5/4(x - (-4))
First, simplify the equation by simplifying the expressions inside the parentheses:
y - 6 = -5/4(x + 4)
Next, distribute -5/4 to both terms inside the parentheses:
y - 6 = -5/4x - 20/4
Simplify -20/4 to -5:
y - 6 = -5/4x - 5
This is the equation in point-slope form for the line passing through the point (-4, 6) with a slope of -5/4.
well, did you look at the formula? If a line with slope m passes through (h,k), its equation is
y-k = m(x-h)
So plug in your numbers.