Qual è l'equazione della linea che passa attraverso (3, -7) e (-2, 4)?
Risposta:
#y=-11/5x-2/5#
Spiegazione:
#"the equation of a line in "color(blue)"slope-intercept form"# is.
#color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))#
#"where m is the slope and b the y-intercept"#
#"to calculate m use 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)|)))#
#"let "(x_1,y_1)=(3,-7)" and "(x_2,y_2)=(-2,4)#
#rArrm=(4-(-7))/(-2-3)=11/(-5)=-11/5#
#rArry=-11/5x+blarr" partial equation"#
#"to find b substitute either of the 2 given points into"#
#"the partial equation"##"using "(-2,4)#
#4=22/5+brArrb=-2/5#
#rArry=-11/5x-2/5larrcolor(red)" in slope-intercept form"#