How do you write the equation of a line in slope intercept, point slope and standard form given (3,-2) and has the slope of 3/4?

The equation of a line in #color(blue)"point-slope form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(y-y_1=m(x-x_1))color(white)(2/2)|)))#
where m represents the slope and # (x_1,y_1)" a point on the line"#

#"here "m=3/4" and " (x_1,y_1)=(3,-2)#

substituting these values into the equation gives.

#y-(-2)=3/4(x-3)#

#rArry+2=3/4(x-3)larrcolor(red)" in point-slope form"#

The equation 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 represents the slope and b, the y-intercept.

distribute and simplify the point-slope equation into this form.

#rArry+2=3/4x-9/4#

#y=3/4x-9/4-2#

#rArry=3/4x-17/4larrcolor(red)" in slope-intercept form"#

The equation in #color(blue)"standard form"# is.

#color(red)(bar(ul(|color(white)(2/2)color(black)(Ax+By=C)color(white)(2/2)|)))#
where A is a positive integer and B ,C are integers.

Rearrange the slope-intercept equation into this form.

#3/4x-y=17/4larr" multiply through by 4"#

#rArr3x-4y=17larrcolor(red)" in standard form"#