Question

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

Answer 1

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**.