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Answer:
[tex]y=-\frac{4}{3} x-\frac{14}{3}[/tex]
Step-by-step explanation:
Linear equations are typically organized in slope-intercept form:
[tex]y=mx+b[/tex] where m is the slope and b is the y-intercept (the value of y when the line crosses the y-axis)
1) Determine the slope (m)
Parallel lines will always have the same slope. Therefore, this line will have the same slope as the given line [tex]y=-\frac{4}{3} x+ \frac{7}{3}[/tex].
Plug in [tex]-\frac{4}{3}[/tex] as the slope
[tex]y=-\frac{4}{3} x+b[/tex]
2) Determine the y-intercept (b)
To find the y-intercept, plug the given point (-5,2) into the equation and solve for b.
[tex]2=-\frac{4}{3}(-5)+b\\2=\frac{20}{3}+b[/tex]
Subtract both sides by [tex]\frac{20}{3}[/tex]
[tex]2-\frac{20}{3} = \frac{20}{3}+b-\frac{20}{3}\\\frac{6}{3} -\frac{20}{3}=b\\-\frac{14}{3} = b[/tex]
Therefore, the y-intercept is [tex]-\frac{14}{3}[/tex].
3) Plug the y-intercept back into our original equation
[tex]y=-\frac{4}{3} x-\frac{14}{3}[/tex]
I hope this helps!