lines

2x + 3y = -5    re-arrange

3y = -2x - 5

y  =  -2/3 x  - 5/3       slope = -2/3       perpindicular slope =   -  1  / (-2/3)  = 3/2

y = 3/2 x + b    sub in the given point to find 'b'

1 = 3/2(-6) + b         b = 10

y = 3/2 x  + 10

What is the slope-intercept form of the equation of the line that passes through the point (-6, 1) and is perpendicular to the graph of 2x + 3y = -5?

Was ist die Steigungsschnittform der Gleichung der Linie, die durch den Punkt (-6, 1) verläuft und senkrecht zum Graphen von 2x + 3y = -5 ist?

Hello Guest!

\(\color{BrickRed} 2x + 3y = -5\\ y=-\frac{2}{3}x-\frac{5}{3}\\ m_1=-\frac{2}{3}\\ \color{blue}m_2=\frac{3}{2}\)

\(y=m_2(x-x_1)+y_1\\ y=1.5(x+6)+1\)

The slope-intercept form of the equation  that passes through the point (-6, 1) is

\(y=1.5x+10\)

  !