Question

How do you graph $ 2x + y = 3 $ ?

Answer 1

Hint: To solve this problem, we have to arrange the terms similar to the straight-line equation which is equal to, $ y = mx + c $ compare the given equation with straight line equation. Find slope $ m $ and $ y - \operatorname{int} ercept(c) $ . And at last, put $ y = 0 $ and find the value of $ x $ . Plot the point in the graph.

Complete step-by-step answer:
Let us consider the given equation,
 $ 2x + y = 3 $
We know that, the equation for straight line is $ y = mx + c $ and now I am rearranging the terms of the given equation similar to the straight-line equation and by doing this we get,
 $ y = - 2x + 3 $ … (1)
Compare the above equation with straight line equation, the coefficient of $ x $ will be the slope of this equation and the constant term $ 3 $ is the y-intercept and by comparing we get the value of slope $ m = - 3 $ and y-intercept $ c = 3 $ . The value of the slope is negative.
Now to find the value of $ x $ , put $ y = 0 $ in (1) we get,
 $
  0 = - 2x + 3 \\
  2x = 3 \\
  x = 1.5 \;
  $
We get $ x = 1.5 $
And the points are $ $
 The horizontal axis is called $ x - axis $ and the vertical axis is called $ y - axis $ .We have two points which is $ (0,3),(1.5,0) $ . Plot these points in the graph and by joining these we form a straight line. Because it is actually a straight-line equation and so we will get a straight line by joining all these points.

Note: The equation of the straight line is $ y = mx + c $ , where $ m $ is the slope or gradient of the straight line, $ c $ is the value of $ y $ when $ x = 0 $ , $ x $ is the direction of how far along it is moving and $ y $ is the value of how far it is rising.