Question

Through: (5,3), perpendicular to y=-5/7x-2

Answer 1

The equation of the perpendicular line through the given point is;

$y\text{ = }\frac{7}{5}x-4$

Here, we want to get the equation of a line that is perpendicular to the given line and passes through the given point

Mathematically, if two lines are perpendicular, the product of their slopes is -1

Generally, the equation of a straight line can be written as;

$y\text{ = mx + b}$

where m is the slope and b is the y-intercept

With respect to the equation given, the slope is -5/7

Now, to get the slope of the second line, we have that;

$\begin{gathered} m_1\times m_2\text{ = -1} \\ \frac{-5}{7}\times m_2\text{ = -1} \\ \\ m_2\text{ = }\frac{-7}{-5} \\ m_{2_{}\text{ }}\text{ = }\frac{7}{5} \end{gathered}$

Since we have the slope of the second line and the point it passes through, we can write its equation using the point-slope form

Mathematically, we have this as;

$\begin{gathered} y-y_1=m(x-x_1) \\ y-3\text{ = }\frac{7}{5}(x-5) \\ \\ y-3\text{ = }\frac{7}{5}x\text{ - }7 \\ \\ y=\text{ }\frac{7}{5}x-7+3 \\ y\text{ = }\frac{7}{5}x-4 \end{gathered}$