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Answer:
An equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12 will be:
Step-by-step explanation:
Given the equation
[tex]5x - y = 12[/tex]
converting the line into the slope-intercept form y = mx+b, where m is the slope
[tex]-y = 12-5x[/tex]
[tex]y = 5x-12[/tex]
The slope of the line = m = 5
We know that a line perpendicular to another line contains a slope that is the negative reciprocal of the slope of the other line, such as:
Therefore, the slope of new line = – 1/m = -1/5 = -1/5
Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the slope of new line = -1/5 and (-2, 3)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y-3=-\frac{1}{5}\left(x-\left(-2\right)\right)[/tex]
[tex]y-3=-\frac{1}{5}\left(x+2\right)[/tex]
Add 3 to both sides
[tex]y-3+3=-\frac{1}{5}\left(x+2\right)+3[/tex]
[tex]y=-\frac{1}{5}x+\frac{13}{5}[/tex]
Therefore, an equation of the line passing through (-2, 3) and perpendicular to the line 5x - y = 12 will be: