Question

HELP ASAP

Answer 1

Answer:

$y = \displaystyle \frac{5}{2}\, x + 54$.

(Equivalently, $5\, x - 2\, y = 108$.)

Step-by-step explanation:

Rewrite the equation of the line $2\, x + 5\, y = 10$ in the slope-intercept form $y = m\, x + b$ to find the slope $m$.

$5\, y = -2\, x + 10$.

$\displaystyle y = -\frac{2}{5}\, x + 2$.

Therefore, the slope of the line $2\, x + 5\, y = 10$ is $(-2 / 5)$.

Let $m_1$ and $m_2$ denote the slope of two lines on a cartesian plane. If these two lines are perpendicular to one another, then $m_1 \cdot m_2 = (-1)$.

In this question, the slope of the first line was already found $m_1 = (-2 / 5)$. Solve $m_1 \cdot m_2 = (-1)$ for the slope $m_2$ of the unknown line:

$\begin{aligned}m_2 &= \frac{-1}{m_1} = \frac{-1}{-2 / 5} = \frac{5}{2}\end{aligned}$.

The following information are thus available for the requested line:

• The slope of this line is $\displaystyle m = \frac{5}{2}$.
• This line contains the point $(x_0,\, y_0) = (-20,\, 4)$.

Hence, the point-slope form $(y - y_0) = m\, (x - x_0)$ would be a possible choice for the equation of this line:

$\displaystyle y - 4 = \frac{5}{2}\, (x - (-20))$.

Simplify to obtain the slope-intercept form equation of this line:

$\displaystyle y = \frac{5}{2}\, x + 54$.

Equivalently:

$5\, x - 2\, y = 108$.