Does the line through the points (2,2) and (3,4) intersect the line through the points (-1,5) and (0,7)? Explain your response

1 Answer
Jim G.
Jan 21, 2018

#"no intersection"#

Explanation:

#• " parallel lines have equal slopes"#

#"calculate the slopes of the lines going through the "#
#"given points using the "color(blue)"gradient formula"#

#color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))#

#"using "(x_1,y_1)=(2,2)" and "(x_2,y_2)=(3,4)#

#m=(4-2)/(3-2)=2/1=2#

#"slope of line through these points is "m=2#

#"using "(x_1,y_1)=(-1,5)" and "(x_2,y_2)=(0,7)#

#m=(7-5)/(0+1)=2/1=2#

#"the slope of the line going through these points is "m=2#

#"this indicates that the lines are parallel and never intersect"#
graph{(y-2x+2)(y-2x-7)=0 [-10, 10, -5, 5]}

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