"the equation of a line in "color(blue)"slope-intercept form"the equation of a line in slope-intercept form is.
•color(white)(x)y=mx+b∙xy=mx+b
"where m is the slope and b the y-intercept"where m is the slope and b the y-intercept
"to calculate m use the "color(blue)"gradient formula"to calculate m use the gradient formula
•color(white)(x)m=(y_2-y_1)/(x_2-x_1)∙xm=y2−y1x2−x1
"let "(x_1,y_1)=(-5,6)" and "(x_2,y_2)=(4,2)let (x1,y1)=(−5,6) and (x2,y2)=(4,2)
rArrm=(2-6)/(4-(-5))=(-4)/9=-4/9⇒m=2−64−(−5)=−49=−49
rArry=-4/9x+blarrcolor(blue)"is the partial equation"⇒y=−49x+b←is the partial equation
"to find b substitute either of the 2 given points into"to find b substitute either of the 2 given points into
"the partial equation"the partial equation
"using "(4,2)" then"using (4,2) then
2=-16/9+brArrb=18/9+16/9=34/92=−169+b⇒b=189+169=349
rArry=-4/9x+34/9larrcolor(red)"in slope-intercept form"⇒y=−49x+349←in slope-intercept form
