Question

question 23 what is an equation of the line that passes through the point (-4,4) and is perpendicular to the line 4x - 5y = 10? answer

Explanation:

Step1: Find the slope of the given line

Rewrite the line $4x - 5y=10$ in slope - intercept form $y = mx + b$ ($m$ is the slope). We get $y=\frac{4}{5}x - 2$, so the slope of this line $m_1=\frac{4}{5}$.

Step2: Determine the slope of the perpendicular line

If two lines are perpendicular, the product of their slopes is $- 1$. Let the slope of the required line be $m_2$. Then $m_1\times m_2=-1$. Substituting $m_1 = \frac{4}{5}$, we have $\frac{4}{5}m_2=-1$, so $m_2=-\frac{5}{4}$.

Step3: Use the point - slope form to find the equation of the line

The point - slope form of a line is $y - y_1=m(x - x_1)$, where $(x_1,y_1)=(-4,4)$ and $m = -\frac{5}{4}$. Substitute these values: $y - 4=-\frac{5}{4}(x + 4)$.
Expand it: $y-4=-\frac{5}{4}x-5$.
Move the terms to get the general form: $y=-\frac{5}{4}x - 1$ or $5x+4y=-4$.

Answer:

$y = -\frac{5}{4}x - 1$ (or $5x + 4y=-4$)