Respuesta :
An equation to the line is parallel to other equations if they have the same slope. This slope can be determine if the equation is in the slope-intercept form.
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given the equation 2x - y = -1, convert this equation to slope intercept form.
[tex]\begin{gathered} 2x-y=-1 \\ -y=-2x-1 \\ \text{Divide all terms by negative and we get} \\ y=2x+1 \\ \text{The slope }m\text{ is equal to 2, therefore, we need to find equations whose slope is also} \\ \text{equal to 2} \end{gathered}[/tex]2x + y = 8
[tex]\begin{gathered} \text{Convert to slope intercept form} \\ 2x+y=8 \\ y=-2x+8 \\ \text{slope is }-2 \end{gathered}[/tex]y = -1/2x + 3, this is already in the slope intercept form where the slope is -1/2.
y - 1 = 2(x-3)
[tex]\begin{gathered} y-1=2(x-3) \\ y=2x-6+1 \\ y=2x-5 \\ \text{the slope is }2 \end{gathered}[/tex]y = -2x - 1, is already in the slope-intercept form with a slope of -2
Conclusion
Out of 4 equations, the equation with the same slope as the given which is 2, is the equation
[tex]y-1=2(x+3)[/tex]