Question

here is an equation.
2x - 1 = 5
draw a graph to help solve the equation. then find the solution to the equation.

Explanation:

Step1: Rearrange to find $y_1$ and $y_2$

Treat the equation as two functions: $y_1 = 2x - 1$ and $y_2 = 5$.

Step2: Plot $y_2 = 5$

This is a horizontal line passing through $(0, 5)$ (all points where $y=5$).

Step3: Plot $y_1 = 2x - 1$

Find two points: when $x=0$, $y_1 = 2(0)-1 = -1$ (point $(0, -1)$); when $x=1$, $y_1 = 2(1)-1 = 1$ (point $(1, 1)$). Draw a line through these points.

Step4: Find intersection of lines

The intersection of $y_1=2x-1$ and $y_2=5$ is where $2x-1=5$. Solve for $x$:
$$2x = 5 + 1$$
$$2x = 6$$
$$x = \frac{6}{2} = 3$$
The intersection point is $(3, 5)$.

Answer:

The solution to the equation $2x-1=5$ is $x=3$. The graph has a horizontal line $y=5$ and a line $y=2x-1$ intersecting at $(3, 5)$.