Slope intercept form is:" "y=mx+c y=mx+c
where mm is the gradient and cc is the y-intercept.
Gradient->("change in y")/("change in x")→change in ychange in x
Let point 1 be P_1->(x_1,y_1)=(5,1)P1→(x1,y1)=(5,1)
Let point 2 be P_2->(x_2,y_2)=(3,-2)P2→(x2,y2)=(3,−2)
Thus Gradient ->(y_2-y_1)/(x_2-x_1)= (-2-1)/(3-5) =(-3)/(-2)=+3/2→y2−y1x2−x1=−2−13−5=−3−2=+32
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So now we have y=3/2x+cy=32x+c
To find the value of cc we substitute in the value of a known point so that there is only 1 unknown.
color(brown)(=>P_1->y_1=3/2x_1+c)color(blue)( -> 1=3/2(5)+c)⇒P1→y1=32x1+c→1=32(5)+c
" "1=15/2+c 1=152+c
Subtract color(magenta)(15/2)152 from both sides
" "color(blue)(1color(magenta)(-15/2)=15/2 color(magenta)(-15/2)+c 1−152=152−152+c
c=-13/2c=−132
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" "bar(ul(|color(white)(.)y=3/2x-13/2color(white)(.)|))
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