Question

a line that includes the point (1, 4) has a slope of \\(\frac{1}{2}\\). what is its equation in point - slope form?\
use the specified point in your equation. write your answer using integers, proper fractions, and improper fractions. simplify all fractions.\
\\(y - \square = \square(x - \square)\\)

Explanation:

Step1: Recall point - slope formula

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $(x_1,y_1)$ is a point on the line and $m$ is the slope of the line.

Step2: Identify values of $x_1$, $y_1$ and $m$

We are given the point $(1,4)$, so $x_1 = 1$ and $y_1=4$. The slope $m=\frac{1}{2}$.

Step3: Substitute values into the formula

Substitute $x_1 = 1$, $y_1 = 4$ and $m=\frac{1}{2}$ into the point - slope formula $y - y_1=m(x - x_1)$. We get $y - 4=\frac{1}{2}(x - 1)$.

Answer:

$y - 4=\frac{1}{2}(x - 1)$