Use the slope-intercept form to write the equation of the line passing through the point $P ( 28,0 )$ and having the slope $m = - \frac { 1 } { 2 }$. Express the answer in general form.
A) $\quad x - 2 y = - 14$
B) $\quad x - 2 y = 28$
C) $\quad x + 2 y = 28$
D) $\quad y = \frac { 1 } { 2 } x + 1$
E) $\quad x + 2 y = - 28$

Question

Quizplus · Accepted Answer

The slope-intercept form of a line is given by $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. We know the slope, $m=-\frac{1}{2}$, and a point on the line, $P=(28,0)$. We can plug these values into the equation $y=mx+b$ and solve for $b$: $$0=-\frac{1}{2}(28)+b$$ $$0=-14+b$$ $$b=14$$ Therefore, the equation of the line in slope-intercept form is $y=-\frac{1}{2}x+14$. To express the answer in general form, we can rearrange the equation to get it in the form $Ax+By=C$: $$y=-\frac{1}{2}x+14$$$$\Rightarrow 2y=-x+28$$$$\Rightarrow x+2y=28$$ So the answer is $\boxed{	extbf{(C)}}$.

Use the Slope-Intercept Form to Write the Equation of the Line