Final answer:
To find an equation of a line perpendicular to 5x + 2y = 12, we first express the given equation in slope-intercept form to identify its slope. Then, we take the negative reciprocal of the slope to find the perpendicular slope. Any line with the slope 2/5 will be perpendicular to the given line.
Step-by-step explanation:
The question asks for an equation that represents a line perpendicular to the given line 5x + 2y = 12. To find a line perpendicular to another, we need to determine the negative reciprocal of the original line's slope. First, let's put the given equation in slope-intercept form (y = mx + b) to easily identify its slope.
5x + 2y = 12
2y = -5x + 12
y = (-5/2)x + 6
The slope of this line is -5/2. The negative reciprocal of -5/2 is 2/5. Therefore, the slope of the line perpendicular to the original line is 2/5. Now we can construct the new equation with this slope, which would look like y = (2/5)x + b. Without a specific point through which this new line must pass, we cannot determine the exact value of b, the y-intercept. However, any line of the form y = (2/5)x + c, where c is any real number, will be perpendicular to the original line.