how do plot the equation 4x+y=0 when graphing lines in standard form or explain how to break the equation down

Thank you for the opportunity to help you with your question!

standard form of equation is

y = mx + c

where m is the slope of the line and c is the y intercept( the point at which the line touches y axis)

here 4x+y=0

y = -4x + 0

comparing this with standard equation

slope , m = -4 and y intercept , c = 0

so draw a line which has slope - 4 and passes through 0 in y axis( that means origin here)

grapher.gif

graph is plotted above

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