# Find an equation of the line that passes through the point (-5,7) and is parallel to y=4-3x

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The required equation is:[tex]y=-3x-8[/tex]Step-by-step explanation:We need to find an equation of the line that passes through the point (-5,7) and is parallel to [tex]y=4-3x[/tex]Finding Slope of required line:The given equation is: [tex]y=4-3x[/tex]Rearranging in slope intercept form: [tex]y=-3x+4[/tex]Comparing to standard slope intercept form [tex]y=mx+b[/tex] where m is slope, the slope is -3.Since the lines are parallel and parallel lines have same slope of slope m= -3Finding y-intercept (b):We have slope = -3 and point(-5,7) where x = -5 and y =7Putting values in the formula of slope intercept form:[tex]y=mx+b\\7=-3(-5)+b\\7=15+b\\b=7-15\\b=-8[/tex]So, value of b = -8.Putting value of slope and y-intercept to find the required equation:[tex]y=mx+b\\y=-3x-8[/tex]So, The required equation is:[tex]y=-3x-8[/tex]Keywords: Equation of lines
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