Question

Which equation represents a line that passes through (5, 1) and has a slope of 1/2 ?

Answer 1

Answer:

Point-slope equation of this line:

$\displaystyle y - 1 = \frac{1}{2}(x-5)$.

Step-by-step explanation:

The equation for a line in a cartesian plane can take multiple forms. This question gives

• a point on the line, and
• the slope of the line.

The point-slope form will the most appropriate.

What is the point-slope form equation of a line $l$?

In general,

$l:\; y - y_0 = m (x - x_0)$,

where

• $x_0$ is the x-coordinate of the given point on the line,
• $y_0$ is the y-coordinate of the given point on the line, and
• $m$ is the slope or gradient of the line.

In other words, $(x_0,\; y_0)$the point on the line.

For this line,

• The point is $(5,\;1)$, where $x_0 = 5$ and $y_0 = 1$.
• Gradient of the line $\displaystyle m = \frac{1}{2}$.

Thus the equation for this line:

$\displaystyle y - 1 = \frac{1}{2} (x - 5)$.