how do you find the solution to a system of equations graphically.
find the slope of the two lines
find the point where the two lines intersect
find the y-intercept of the two lines
find the slope and y-intercept of the two lines
To find the solution to a system of equations graphically, you will need to graph both equations on the same set of axes and look for the point where the two lines intersect. Here's a step-by-step guide on how to do that:
1. Start by rewriting the equations in the form y = mx + b, where m represents the slope and b represents the y-intercept.
2. Once you have the equations in slope-intercept form, identify the slope of each line. The slope is the coefficient of x in each equation.
3. Next, locate the y-intercept for each line. The y-intercept is the value of y when x = 0. It is represented by the constant term (b) in each equation.
4. Plot the y-intercept for each line on the y-axis.
5. Using the slope, determine the second point on each line. The slope defines the change in y divided by the change in x, so you can move up or down and left or right based on the slope value.
6. Connect the plotted points on each line with a straight line.
7. The solution to the system of equations is the point where the two lines intersect. This point represents the values of x and y that satisfy both equations simultaneously.
Finding the slope and y-intercept of each line will help you graph the equations accurately. By examining the equations in slope-intercept form, you can read off the slope and y-intercept values. Once you have plotted the lines, the point of intersection will provide the solution to the system of equations.