"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+c∙xy=mx+c
"where m is the slope and c the y-intercept"where m is the slope and c 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)=(3,5)" and "(x_2,y_2)=(2,-2)let (x1,y1)=(3,5) and (x2,y2)=(2,−2)
m=(-2-5)/(2-3)=(-7)/(-1)=7m=−2−52−3=−7−1=7
y=7x+clarrcolor(blue)"is the partial equation"y=7x+c←is the partial equation
"to find c substitute either of the 2 given points into"to find c substitute either of the 2 given points into
"the partial equation"the partial equation
"using "(3,5)" then"using (3,5) then
5=21+crArrc=5-21=-165=21+c⇒c=5−21=−16
y=7x-16larrcolor(red)"equation in slope-intercept form"y=7x−16←equation in slope-intercept form
