Final answer:
To find the equation of a line perpendicular to y=-3x+7 and passing through (3,5), we need to calculate the negative reciprocal of the slope of the original line. The equation of the perpendicular line, in slope-intercept form, is y=(1/3)x+4.
Step-by-step explanation:
To find an equation of a line perpendicular to another line, we need to determine the slope of the original line and then find the negative reciprocal of that slope. The given equation is y = -3x + 7, which has a slope of -3. The negative reciprocal of -3 is 1/3. Therefore, the slope of the perpendicular line is 1/3.
We are also given that the line passes through the point (3,5). Using the point-slope form of the equation, y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values into the equation:
y - 5 = (1/3)(x - 3)
Next, we can simplify the equation to slope-intercept form, y = mx + b, by distributing 1/3 to x and moving -5 to the other side:
y = (1/3)x + (5 - 1/3 * 3)
y = (1/3)x + (5 - 1) = (1/3)x + 4
Therefore, the equation of the line that passes through (3,5) and is perpendicular to y = -3x + 7 is y = (1/3)x + 4.