To find the equation of a line that passes through the point (10, 3) and is perpendicular to the line given by the equation y = 5x + 7, we first need to determine the slope of the given line.
The equation of the line y = 5x + 7 can be expressed in slope-intercept form (y = mx + b), where m represents the slope. From this equation, we can see that the slope (m) is 5.
Two lines are perpendicular if the product of their slopes is -1. Therefore, if the slope of the given line is 5, the slope of the line we are looking for will be the negative reciprocal of 5. The negative reciprocal of 5 is -1/5.
Now that we have the slope of the line we want to find, we can use the point-slope form of the equation of a line, which is given by:
y – y1 = m(x – x1)
In this formula, (x1, y1) is the point the line passes through (in this case, (10, 3)), and m is the slope we just calculated (-1/5).
Substituting the values into the point-slope form, we have:
y – 3 = -1/5(x – 10)
Now, we can simplify the equation:
y - 3 = -1/5x + 2By adding 3 to both sides, we get:
y = -1/5x + 5Thus, the equation of the line that passes through the point (10, 3) and is perpendicular to the line given by y = 5x + 7 is:
y = -1/5x + 5.