how do you graph linear equation 2x= -10y and x+5y=3
pick two x values, figure the y values there, and plot the points. Then draw a line between them.
Easy points to pick are where x=0 or y=0.
2x = -10y
(0,0) is on the line.
If x=5, y=-1, so (5,-1) is on the line
Plot those two points and draw a line through them.
x+5y=3
(3,0) is on the line
(-12,3) is on the line
plot and draw.
To graph linear equations, we usually use the slope-intercept form, which is y = mx + b, where m represents the slope and b is the y-intercept. However, the given equations are not in this form, so we need to convert them first.
1. Graphing the equation 2x = -10y:
To convert this equation to slope-intercept form, isolate y:
2x = -10y
Divide both sides by -10:
(2x) / (-10) = y
Simplify:
y = -1/5x
Now we have the equation in slope-intercept form, y = -1/5x. The slope is -1/5, and the y-intercept is 0.
To graph this equation, start by plotting the y-intercept, which is the point (0, 0). Next, use the slope to find additional points. Since the slope is -1/5, you can move down one unit on the y-axis and to the right five units on the x-axis to find another point. Connect these points to draw a straight line. The line represents all the possible solutions to the equation.
2. Graphing the equation x + 5y = 3:
Again, let's convert this equation to slope-intercept form:
x + 5y = 3
Subtract x from both sides:
5y = -x + 3
Divide both sides by 5:
(5y) / 5 = (-x + 3) / 5
Simplify:
y = -1/5x + 3/5
Now we have the equation in slope-intercept form, y = -1/5x + 3/5. The slope is -1/5, and the y-intercept is 3/5.
To graph this equation, start by plotting the y-intercept, which is the point (0, 3/5). Next, use the slope to find additional points. Since the slope is -1/5, you can move down one unit on the y-axis and to the right five units on the x-axis to find another point. Connect these points to draw a straight line. The line represents all the possible solutions to the equation.
Now you have two lines graphed. The point where these lines intersect, if any, represents the solution to the system of equations.