How do you find the solution to a system of equations graphically?(1 point)
Find the slope of the two lines.
Find the slope and y-intercept of the two lines.
Find the y-intercept of the two lines.
Find the point where the two lines intersect.
Find the point where the two lines intersect.
To find the solution to a system of equations graphically, you can follow these steps:
1. Find the slope of the two lines:
- The slope of a line can be determined by identifying the change in the y-values (vertical change) divided by the change in the x-values (horizontal change) between any two points on the line.
2. Find the slope and y-intercept of the two lines:
- The slope-intercept form of a linear equation is y = mx + b, where m represents the slope and b represents the y-intercept.
3. Find the y-intercept of the two lines:
- The y-intercept is the point where the line crosses the y-axis. It determines the value of y when x = 0.
4. Find the point where the two lines intersect:
- The point of intersection is where the two lines cross each other. To find this point, set the equations equal to each other and solve for the values of x and y that make both equations true.
Remember, these steps are specific to solving a system of equations graphically.
To find the solution to a system of equations graphically, you can follow the steps below:
1. Find the slope of the two lines:
- The slope of a line can be determined by finding the change in y-coordinates (rise) divided by the change in x-coordinates (run) between any two points on the line.
2. Find the slope and y-intercept of the two lines:
- To determine the slope-intercept form (y = mx + b) of each line, you need the slope and the y-intercept. The slope is the coefficient of the x-term (m), and the y-intercept is the constant term (b).
3. Find the y-intercept of the two lines:
- To find the y-intercept, you can set x = 0 in the equation of each line and solve for y. The resulting value of y will give you the y-coordinate where the line intersects the y-axis.
4. Find the point where the two lines intersect:
- The solution to the system of equations is the point where the two lines intersect. This point will satisfy both equations simultaneously. You can either visually identify the point of intersection on the graph or find the coordinates by solving the system of equations algebraically (e.g., substitution or elimination method).
Keep in mind that these steps are specific to finding the solution graphically. There are also other methods, such as substitution or elimination, to find the solution algebraically.