Respuesta :
Let's find the y-intercept of the line with equation
[tex]-7x+6y=-3[/tex]To get the y-intercept, we plug in "0" into "x". So,
[tex]\begin{gathered} -7x+6y=-3 \\ -7(0)+6y=-3 \\ 6y=-3 \\ y=\frac{-3}{6} \\ y=-\frac{1}{2} \end{gathered}[/tex]So, the coordinate point is
[tex](0,-\frac{1}{2})[/tex]We need to find the equation of the line that is perpendicular to the line with equation -2x + 4y = 2 and passes through the point (0, -1/2).
First, let's re-arrange -2x + 4y = 2 into the form y = mx + b, where m is the slope and b is the y-intercept.
[tex]\begin{gathered} -2x+4y=2 \\ 4y=2x+2 \\ y=\frac{2x}{4}+\frac{2}{4} \\ y=\frac{1}{2}x+\frac{1}{2} \end{gathered}[/tex]We know the line perpendicular will have a slope that is negative reciprocal.
So, the perpendicular line will have a slope of
[tex]-2[/tex]So, the line will take the form:
[tex]y=-2x+b[/tex]Since it goes through the point (0, -1/2), we can solve for "b":
[tex]\begin{gathered} y=-2x+b \\ -\frac{1}{2}=-2(0)+b \\ -\frac{1}{2}=b \\ \end{gathered}[/tex]Thus, the equation of the linne is,
[tex]y=-2x-\frac{1}{2}[/tex]