# Write a linear equation that does not intersect the graph of y=-2x+3 and has an x-intercept of 1. Explain your reasoning.

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Answer:[tex]\newline{\text{The equaiton of the line is y=-2x+2}}[/tex]Step-by-step explanation:[tex]\newline{\text{If 2 lines to not intersect, then those 2 lines are paralell.}}[/tex][tex]\bigskip\newline{\text{Also, the x-intercept is where the line crosses the x axis or where y=0.}}[/tex][tex]\bigskip\newline{\text{We need to find 2 lines that are paralell and have an x intercept of 1}}[/tex][tex]\bigskip\bigskip\newilne{\text{Paralell lines have the same slope}}[/tex][tex]\bigskip\newline{\text{For y=mx+b, m is the slope}}[/tex][tex]\bigskip\newline{\text{Since our original equation was y=-2x+3, the slope is -2}}[/tex][tex]\bigskip\newline{\text{Paralell lines have same slope so our mystery line is y=-2x+b where b is a constant}}[/tex][tex]\bigskip\newline{\text{To find the value of b, we can use the 'point' given by the x-intercept}}[/tex][tex]\bigskip\newline{\text{x-intercept of 1 means that when y=0, x=1, so (1,0) is a point that is true}}[/tex][tex]\bigskip\newline{\text{Find the value of b that makes y=-2x+b true for (1,0)}}\bigskip\newline{\text{Subsitute 1 for x and 0 for y}}\bigskip\newline{0=-2(1)+b}\bigskip\newline{0=-2+b}[/tex][tex]\bigskip\newline{2=b}\bigskip\bigskip\newline{\text{The equation of the line is y=-2x+2}}[/tex]

Answer:y =-2x+2 Step-by-step explanation:We want a line that does not intersect y = -2x+3It must be parallel to this line, so it must have the same slope (Parallel lines have the same slope)The slope is -2We have an x intercept of 1 (1,0)The have the slope and a pointWe can use the point slope form of a line to write the equationy-y1 = m(x-x1)y-0 = -2(x-1)Distributey=-2x+2y =-2x+2 This is in slope intercept form