Answer:
The equation of the line that passes through the point (-2, -3) and is perpendicular to the line will be:
Step-by-step explanation:
Given the line
[tex]x+3y=24[/tex]
The slope-intercept form
[tex]y = mx+b[/tex]
where m is the slope and b is the y-intercept
Writing the line equation in the slope-intercept form
[tex]x+3y=24[/tex]
[tex]y=-\frac{1}{3}x+8[/tex]
Thus, the slope = m = -1/3
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:
slope = m = -1/3
perpendicular slope = – 1/m
[tex]=-\frac{1}{-\frac{1}{3}}=3[/tex]
Using the point-slope of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
substituting perpendicular slope = 3 and (x₁, y₁) = (-2, -3)
[tex]y-\left(-3\right)=3\left(x-\left(-2\right)\right)[/tex]
[tex]y+3=3\left(x+2\right)[/tex]
subtract 3 from both sides
[tex]y+3-3=3\left(x+2\right)-3[/tex]
[tex]y=3x+3[/tex]
Therefore, the equation of the line that passes through the point (-2, -3) and is perpendicular to the line will be:
