Which equation represents a line that passes through $(5,1)$ and has a slope of $\frac{1}{2}$?

A. $y-5=\frac{1}{2}(x-1)$
B. $y-\frac{1}{2}=5(x-1)$
C. $y-1=\frac{1}{2}(x-5)$
D. [tex]$y-1=5\left(x-\frac{1}{2}\right)$[/tex]

Certainly! Let's find the equation of a line that passes through the point $(5,1)$ and has a slope of $\frac{1}{2}$.

We will use the point-slope form of the equation of a line, which is given by:

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

Here, $(x_1, y_1)$ is a point on the line and $m$ is the slope.

Given:
- The point $(x_1, y_1) = (5, 1)$
- The slope $m = \frac{1}{2}$

Substitute the values into the point-slope form:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]

This equation represents the line that passes through the point $(5,1)$ and has a slope of $\frac{1}{2}$.

Among the given choices, the one that matches this equation is:

[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]

Thus, the correct answer is:
[tex]\[ y - 1 = \frac{1}{2}(x - 5) \][/tex]

So, the corresponding choice is:
[tex]\[ \boxed{3} \][/tex]

Which equation represents a line that passes through \((5,1)\) and has a slope of \(\frac{1}{2}\)?A. \(y-5=\frac{1}{2}(x-1)\) B. \(y-\frac{1}{2}=5(x-1)\) C. \(y-1=\frac{1}{2}(x-5)\) D. [tex]\(y-1=5\left(x-\frac{1}{2}\right)\)[/tex]

Answer :

Other Questions

Which equation represents a line that passes through \((5,1)\) and has a slope of \(\frac{1}{2}\)?

A. \(y-5=\frac{1}{2}(x-1)\)
B. \(y-\frac{1}{2}=5(x-1)\)
C. \(y-1=\frac{1}{2}(x-5)\)
D. [tex]\(y-1=5\left(x-\frac{1}{2}\right)\)[/tex]