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melomori [17]
3 years ago
7

Write the slope-intercept form of the equation of the line that passes thrqugh (-4, -3) and is

Mathematics
1 answer:
Zielflug [23.3K]3 years ago
8 0

Answer:

Step-by-step explanation:

Equation of the line y = mx + c

The new line is perpendicular to 2x - 3y = -5

                                         - 3y = - 5 - 2x

                                           3y = 2x + 5

                                            y =\frac{2x}{3} + \frac{5}{3}

Since the lines are perpendicular to each other : m_{1} . m_{2} = -1

where m_{1} \ slope \ of \ the \  given  \ line  \ and  \ m_{2} \  slope \ of \ the  \ new  \line\\.

Slope of the given line

                m_{1} = \frac{2}{3}

Slope of the new line

                \\\frac{2}{3}.m_{2} = -1\\  m_{2} = -1 . \frac{3}{2}   = \frac{-3}{2}

The equation to the new line passing through (-4, -3) and perpendicular to 2x - 3y = -5

                            (y - y_{1}) = m_{2}(x-x_{2} )\\\\(y - (-4)) = \frac{-3}{2}(x - (-3)) \\\\(y + 4) = \frac{-3}{2} (x+ 3)\\\\2(y +4) = -3(x+3)\\\\2y + 8 = -3x -9 \\\\2y = -3x - 9 -8\\\\y = \frac{-3x}{2} - \frac{17}{2}

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