How do you write the standard form of a line given (-2, 4) and has a slope of 1/2?

Question

Ethan Adkins · Accepted Answer

#y=x/2+5#

#m:"slope of line"#
#P:(x,y)"any point of line"#

#"the standard line equation is "y-y_1=m(x-x_1)#

#"given " m=1/2" ; "P(-2,4)" ; "y_1=4" ; "x_1=-2#

#y-4=1/2(x+2)#

#y-4=x/2+1#

#y=x/2+1+4#

#y=x/2+5#

Eli Assouline · Answer

#y=1/2x+5#

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

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

here #m=1/2" and " (x_1,y_1)=(-2,4)#

substitute these values into the equation.

#rArry-4=1/2(x+2)#

distribute the bracket and collect 'like terms'

#y-4=1/2x+1rArry=1/2x+5" is the equation"#

Hazel Anglin · Answer

undefined The standard form of a line can be written as Ax + By = C, where A, B, and C are integers, and A is positive. To find the standard form of a line given a point (-2, 4) and a slope of 1/2, we first need to find the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Using the given point (-2, 4) and the slope 1/2, we can substitute these values into the slope-intercept form equation and solve for the y-intercept b. Once we have the slope-intercept form equation, we can convert it to standard form by rearranging the terms to get all the variables on one side of the equation and the constant on the other side.