Question

Give the equation of a line in slope-intercept form with the following criteria:

Answer 1

Answer:

$y = - \frac{7}{6}x + 9$

Step-by-step explanation:

We need to find a straight line that is perpendicular to the line $y = \frac{6}{7} x + 4$.

So, the slope of the given straight line is $\frac{6}{7}$ {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 $\frac{6}{7} \times (- \frac{7}{6}) = - 1$}

Then the equation of the required straight line in slope-intercept form will be $y = - \frac{7}{6} x + c$ ............. (1) {Where c is any constant}

Now, point (12, -5) will satisfy the equation (1).

Hence, $-5 = - \frac{7}{6}(12) + c$

⇒ - 5 = - 14 + c

⇒ c = 9

Therefore, the complete equation of the required straight line is $y = - \frac{7}{6}x + 9$ (Answer)