Final answer:
To find the line perpendicular to 5x + 2y = 6 that passes through (10, 7), determine the negative reciprocal of the original slope, which is 2/5, and use the point to find the y-intercept, resulting in the equation y = (2/5)x + 3.
Step-by-step explanation:
To find the equation of a line perpendicular to another line, we first need the slope of the given line. For the equation 5x + 2y = 6, we can rewrite it in slope-intercept form to find its slope. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
First, solve the given equation for y:
2y = -5x + 6
y = (-5/2)x + 3
The slope of the given line is -5/2. The slope of a line perpendicular to another is the negative reciprocal of the given line's slope. Thus, the slope of our new line is 2/5. Now, we use the point (10, 7) to find the y-intercept (b) of the new line:
y = mx + b
7 = (2/5)(10) + b
7 = 4 + b
b = 3
The equation of the line satisfying the conditions is:
y = (2/5)x + 3