Question

Find an equation in slope-intercept form of the line satisfying the specified conditions.
Through (8,-3), perpendicular to -6x + 7y=-62.

Answer 1

Answer:

$y = - \frac{7}{6} x + 6 \frac{1}{3}$

Step-by-step explanation:

Slope-intercept form

y= mx +c, where m is the slope and c is the y-intercept.

-6x +7y= -62

Rewriting this equation into the slope-intercept form:

7y= 6x -62

$y = \frac{6}{7} x - \frac{62}{7}$

The product of the slope of 2 perpendicular lines is -1.

Let the slope of the unknown line be m.

$m( \frac{6}{7} ) = - 1$

$m = - 1 \div \frac{6}{7}$

$m = - \frac{7}{6}$

Substitute the value of m into the equation:

$y = - \frac{7}{6} x + c$

To find the value of c, substitute a pair of coordinates into the equation.

When x= 8, y= -3,

$- 3 = - \frac{ 7}{6} (8) + c$

$- 3 = - \frac{28}{3} + c$

$c = \frac{28}{3} - 3$

$c = \frac{19}{3}$

$c = 6 \frac{1}{3}$

Thus, the equation of the line is $y = - \frac{7}{6} x + 6 \frac{1}{3}$.