Answer:
Explanation:
To find an equation of the line that passes through the point (-4, 4) and is perpendicular to the line 4x - 5y = 10, you can follow these steps:
1. First, find the slope of the given line by rearranging the equation into the slope-intercept form (y = mx + b), where "m" is the slope:
4x - 5y = 10
-5y = -4x + 10
y = (4/5)x - 2
The slope of the given line is 4/5.
2. Since the line you're looking for is perpendicular to the given line, its slope will be the negative reciprocal of the given line's slope. The negative reciprocal of 4/5 is -5/4.
3. Now that you have the slope of the new line (-5/4) and a point it passes through (-4, 4), you can use the point-slope form of a line to find its equation:
y - y₁ = m(x - x₁)
Where (x₁, y₁) is the given point, and "m" is the slope.
Plugging in the values:
y - 4 = (-5/4)(x - (-4))
y - 4 = (-5/4)(x + 4)
4. You can then simplify this equation to get it into a standard form (Ax + By = C):
Multiply both sides by -4 to eliminate the fraction:
-4(y - 4) = -5(x + 4)
-4y + 16 = -5x - 20
Rearrange the terms:
5x - 4y = 36
So, the equation of the line that passes through the point (-4, 4) and is perpendicular to the line 4x - 5y = 10 is 5x - 4y = 36.