Write the equation of a line that is perpendicular to the given line and that passes through the given point.
y-3 = 8/3 (x+2); (-2,3)
slope of given line = 8/3
so slope of your new line = -3/8
through (-2,3)
y = 3 = (-3/8)(x+2)
since the original was written in that form, I assume the new one is to be in that same format.
To find the equation of a line that is perpendicular to the given line, we need to determine the slope of the given line. The given equation is in slope-intercept form (y = mx + b), where the slope (m) is the coefficient of x.
In the given equation, the coefficient of x is 8/3, which means the slope of the given line is 8/3.
Since we want to find a line perpendicular to this line, we need to find the negative reciprocal of the slope. The negative reciprocal of 8/3 is -3/8.
Now that we have the slope of the perpendicular line (-3/8), we can use the point-slope form of a line to find its equation. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is the given point through which the line passes.
The given point is (-2, 3). Plugging in the values, the equation becomes:
y - 3 = -3/8 (x - (-2))
Simplifying further:
y - 3 = -3/8 (x + 2)
Now, we can distribute the -3/8 to the terms inside the parentheses:
y - 3 = -3/8x - 3/4
To get the equation in slope-intercept form, we need to isolate y:
y = -3/8x - 3/4 + 3
Simplifying further:
y = -3/8x - 3/4 + 12/4
y = -3/8x + 9/4
Therefore, the equation of a line that is perpendicular to the given line and passes through the point (-2, 3) is y = -3/8x + 9/4.