which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the…

which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4)? select three options.\n□y = -\\frac{2}{5}x - 2\n□2x + 5y = -10\n□2x - 5y = -10\n□y + 4 = -\\frac{2}{5}(x - 5)\n□y - 4 = \\frac{5}{2}(x + 5)

which equations represent the line that is perpendicular to the line 5x - 2y = -6 and passes through the point (5, -4)? select three options.\n□y = -\\frac{2}{5}x - 2\n□2x + 5y = -10\n□2x - 5y = -10\n□y + 4 = -\\frac{2}{5}(x - 5)\n□y - 4 = \\frac{5}{2}(x + 5)

Answer

Explanation:

Step1: Rewrite the given line in slope - intercept form

Rewrite $5x - 2y=-6$ as $y=\frac{5}{2}x + 3$. The slope of this line is $m_1=\frac{5}{2}$.

Step2: Find the slope of the perpendicular line

The slope of a line perpendicular to a line with slope $m_1$ is $m_2=-\frac{2}{5}$ (since $m_1\times m_2=- 1$).

Step3: Use the point - slope form

The point - slope form of a line is $y - y_1=m(x - x_1)$. Given the point $(5,-4)$ and $m =-\frac{2}{5}$, we have $y+4=-\frac{2}{5}(x - 5)$.

Step4: Convert to slope - intercept form

Expand $y+4=-\frac{2}{5}(x - 5)$: $y+4=-\frac{2}{5}x+2$, then $y=-\frac{2}{5}x - 2$.

Step5: Convert to standard form

Starting from $y=-\frac{2}{5}x - 2$, multiply through by 5 to get $5y=-2x - 10$, or $2x + 5y=-10$.

Answer:

A. $y=-\frac{2}{5}x - 2$ B. $2x + 5y=-10$ D. $y + 4=-\frac{2}{5}(x - 5)$