Question

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

Answer 1

Answer:

$\large\boxed{y-1=\dfrac{1}{2}(x-5)\leftarrow\text{point-slope form}}\\\boxed{y=\dfrac{1}{2}x-\dfrac{3}{2}\leftarrow\text{slope-intercept form}}\\\boxed{x-2y=3\leftarrow\text{standard form}}$

Step-by-step explanation:

The point-slope of an equation of a line:

$y-y_1=m(x-x_1)$

We have

the point $(5,\ 1)\to x_1=5,\ y_1=1$

and the slope $m=\dfrac{1}{2}$

Substitute:

$y-1=\dfrac{1}{2}(x-5)$          use distributive property

$y-1=\dfrac{1}{2}x-\dfrac{5}{2}$       add 1 to both sides

$y=\dfrac{1}{2}x-\dfrac{3}{2}$        multiply both sides by 2

$2y=x-3$               subtract x from both sides

$-x+2y=-3$            change the signs

$x-2y=3$