Question

multiple choice 5 points
which equation describes the line that has a slope of -2 and passes through the point (1, 3)?
\\( 2x + y = 1 \\)
\\( 2x + y = 5 \\)
\\( 2x + y = -5 \\)
\\( 2x + y = -1 \\)
clear my selection

Explanation:

Step1: Recall point - slope form

The point - slope form of a linear equation is $y - y_1=m(x - x_1)$, where $m$ is the slope and $(x_1,y_1)$ is a point on the line. Here, $m=- 2$, $x_1 = 1$ and $y_1=3$.
Substitute these values into the point - slope form: $y - 3=-2(x - 1)$

Step2: Simplify the equation

Expand the right - hand side: $y - 3=-2x + 2$
Add 3 to both sides: $y=-2x+2 + 3=-2x + 5$
Rearrange the equation to the form $ax+by = c$: $2x+y=5$

Answer:

$2x + y = 5$ (the option corresponding to $2x + y = 5$)