Respuesta :
Answer:
[tex]y = - \frac{7}{6}x + 9[/tex]
Step-by-step explanation:
We need to find a straight line that is perpendicular to the line [tex]y = \frac{6}{7} x + 4[/tex].
So, the slope of the given straight line is [tex]\frac{6}{7}[/tex] {Since the equation is in slope-intercept form}
Now, the slope of the required straight line will be [tex]- \frac{7}{6}[/tex]
{Since, the product of slopes of two straight line that are perpendicular to each other is -1, and [tex]\frac{6}{7} \times (- \frac{7}{6}) = - 1[/tex]}
Then the equation of the required straight line in slope-intercept form will be [tex]y = - \frac{7}{6} x + c[/tex] ............. (1) {Where c is any constant}
Now, point (12, -5) will satisfy the equation (1).
Hence, [tex]-5 = - \frac{7}{6}(12) + c[/tex]
⇒ - 5 = - 14 + c
⇒ c = 9
Therefore, the complete equation of the required straight line is [tex]y = - \frac{7}{6}x + 9[/tex] (Answer)
