Answer:
The equation of the line passing through the point (2,1) and with center (3,5) is y = 4x - 7.
Step-by-step explanation:
To find the equation of a line with the center (3,5) and passing through (2,1), we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1).
First, let's find the slope (m) using the given points: m = (y2 - y1) / (x2 - x1) = (1 - 5) / (2 - 3) = -4 / -1 = 4.
Now, substitute the values of (x1, y1) = (2, 1) and the slope (m) into the point-slope form: y - 1 = 4(x - 2).
Simplify the equation to obtain the final answer in the slope-intercept form: y - 1 = 4x - 8. y = 4x - 7.
Therefore, the equation of the line is y = 4x - 7.
The complete question is:ith center (3,5) and passing through (2,1). your answer.is: