Respuesta :
Answer: [tex]\text{y} = \frac{7}{3}\text{x}-\frac{2}{3}[/tex]
This is the same as writing y = (7/3)x - 2/3
=======================================================
Explanation:
The given equation is in y = mx+b form
m = -3/7 = slope
b = 4 = y intercept
Flip the fraction for the slope to get -7/3, and flip the sign from negative to positive to get 7/3
The original slope is -3/7 and the perpendicular slope is 7/3. These two slopes multiply to -1.
We want the perpendicular line to go through [tex](\text{x}_1,\text{y}_1) = (2,4)\\\\[/tex]
We'll use the point-slope form to get...
[tex]\text{y} - \text{y}_1 = \text{m}(\text{x}-\text{x}_1)\\\\\text{y} - 4 = \frac{7}{3}(\text{x}-2)\\\\\text{y} - 4 = \frac{7}{3}\text{x}+\frac{7}{3}(-2)\\\\\text{y} - 4 = \frac{7}{3}\text{x}-\frac{14}{3}\\\\\text{y} = \frac{7}{3}\text{x}-\frac{14}{3}+ 4 \\\\\text{y} = \frac{7}{3}\text{x}-\frac{14}{3}+ \frac{12}{3} \\\\\text{y} = \frac{7}{3}\text{x}+\frac{-14+12}{3} \\\\\text{y} = \frac{7}{3}\text{x}-\frac{2}{3} \\\\[/tex]
This equation has a slope of 7/3 and y intercept of -2/3.
