Answer:
Read carefully each step for your fully understand it.
Explanation:
To find the equation of a line that is perpendicular to the line y = 2x - 3 and contains the point (-5, 3), we need to find the slope of the perpendicular line.
To find the slope, we use the negative reciprocal of the slope of the given line. The slope of the given line is 2, so the slope of the perpendicular line is -1/2.
We can then use the point-slope formula to find the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3).
The point-slope formula is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Plugging in the values, we get:
y - 3 = -1/2 (x + 5)
We can then simplify this equation to get the final equation:
y = -1/2 x - 11/2
Therefore, the equation of the line that is perpendicular to y = 2x - 3 and contains the point (-5, 3) is y = -1/2 x - 11/2.