Which is the equation of a line that has a slope of 1 and passes through point (5, 3)?

y = x – 2
y = x + 2
y = x + 3
y = x – 5

1 answer

To find the equation of a line with a slope of 1 that passes through the point (5, 3), we can use the point-slope form of the equation of a line, which is given by:

\[ y - y_1 = m(x - x_1) \]

where \( m \) is the slope, and \( (x_1, y_1) \) is the point on the line.

Here, the slope \( m = 1 \) and the point \( (x_1, y_1) = (5, 3) \).

Plugging in these values into the equation:

\[ y - 3 = 1(x - 5) \]

Simplifying this:

\[ y - 3 = x - 5 \] \[ y = x - 5 + 3 \] \[ y = x - 2 \]

So the equation of the line is:

\[ y = x - 2 \]

From the options provided, the correct answer is:

y = x - 2.