Respuesta :
[tex]y\text{ = -2x + 3}[/tex]Explanation:
Given: point (-2, 7)
The given line is perpendicular to the line we are to find.
For a line to be perpendicular to another, the slope of one will be the negative reciprocal of the other slope.
[tex]\begin{gathered} Equation\text{ of of the given line:} \\ -4y+2x=-3 \\ We\text{ need to write the equation in the form y = mx + b so as to get the slope} \\ -4y\text{ = -2x - 3} \\ \frac{-4y}{-4}\text{ = }\frac{-2x}{-4}-\frac{3}{-4} \\ y\text{ = }\frac{1}{2}x\text{ +}\frac{3}{4} \end{gathered}[/tex][tex]\begin{gathered} from\text{ the equation y = }\frac{1}{2}x\text{ + }\frac{3}{4} \\ m\text{ = }slope\text{ = 1/2} \\ b\text{ = }y-intercept\text{ = 3/4} \end{gathered}[/tex]slope of the line perpendicular to the given line = negative reciprocal of the slope
slope = 1/2
reciprocal of the slope = 2/1 = 2
negative reciprocal = -2
2nd slope = -2
To get the equation of line with slope -2, we will use the point given:
[tex]\begin{gathered} \left(-2,\text{ 7}\right):\text{ x = -2, y = 7} \\ y\text{ = mx + b} \\ 7\text{ = -2}\left(-2\right)\text{ + b} \\ 7\text{ = 4 + b} \\ 7\text{ - 4 = b} \\ b\text{ = 3} \end{gathered}[/tex]Th equation of line Perpendicular to the line -4y + 2x = -3 that passed through the point (-2, 7):
[tex]\begin{gathered} m\text{ = -2, b = 3} \\ y\text{ = mx + b} \\ \\ The\text{ equation:} \\ y\text{ = -2x + 3} \end{gathered}[/tex]