Question 4:
One Solution
When you solve equations with ONE solution…..do you get?
0x = 0 0x = any # x= any # (circle the correct scenario)
What does it mean on a graph to have ONE solution?
5 answers
x = any #
use a mathematical equation to see What does it mean on a graph to have ONE solution?
When a linear equation has one solution, it means that the graph of the equation is represented by a single point. The equation of a line with one solution can be written in the form of y = mx + b, where m is the slope of the line and b is the y-intercept.
For example, the equation y = 2x + 3 has a slope of 2 and a y-intercept of 3. When graphed, this equation will result in a line that intersects the y-axis at the point (0, 3) and has a slope of 2.
Alternatively, a quadratic equation with one solution can be written in the form of y = ax^2 + bx + c, where a, b, and c are constants. The graph of a quadratic equation with one solution will appear as a parabola that touches the x-axis at a single point.
For example, the equation y = (x-1)^2 has a minimum point at (1, 0) and only touches the x-axis at this single point. This represents one solution for the equation.
For example, the equation y = 2x + 3 has a slope of 2 and a y-intercept of 3. When graphed, this equation will result in a line that intersects the y-axis at the point (0, 3) and has a slope of 2.
Alternatively, a quadratic equation with one solution can be written in the form of y = ax^2 + bx + c, where a, b, and c are constants. The graph of a quadratic equation with one solution will appear as a parabola that touches the x-axis at a single point.
For example, the equation y = (x-1)^2 has a minimum point at (1, 0) and only touches the x-axis at this single point. This represents one solution for the equation.
can you use a mathematical equation
Certainly! Let's consider the linear equation y = 2x - 1. This equation represents a line with a slope of 2 and a y-intercept of -1.
If we graph this equation, we will see a straight line that intersects the y-axis at the point (0, -1) and has a slope of 2. The line will only intersect the x-axis at a single point, indicating that there is only one solution to the equation y = 2x - 1.
Therefore, on a graph, having ONE solution means that the equation represents a single point of intersection between the line (or curve) and the x-axis, where the values of x and y satisfy the equation.
If we graph this equation, we will see a straight line that intersects the y-axis at the point (0, -1) and has a slope of 2. The line will only intersect the x-axis at a single point, indicating that there is only one solution to the equation y = 2x - 1.
Therefore, on a graph, having ONE solution means that the equation represents a single point of intersection between the line (or curve) and the x-axis, where the values of x and y satisfy the equation.