Answer:
The answer to the linear equation y = 2x + 6 is (x, y) = (1, 2.5). This means that if we plug in x = 1 into the equation, we get y = 2.5.
Explanation:
To find the solution to the linear equation y = 2x + 6, we can first rewrite the equation in slope-intercept form. This is done by rearranging the equation to have the form y = mx + b, where m is the slope of the line and b is the y-intercept.
In this case, we have y = 2x + 6. To put this equation in slope-intercept form, we need to isolate the y-term on one side of the equation. We can do this by subtracting 2x from both sides, which gives us y - 2x = 6.
Next, we need to divide both sides of the equation by the coefficient of the y-term, which is -2 in this case. This gives us the equation y = -(1/2)x + 3.
Finally, we can plug in any value of x that we want to find the corresponding value of y. For example, if we plug in x = 1, we get y = -(1/2) * 1 + 3 = 2.5. Therefore, the solution to the equation y = 2x + 6 is (x, y) = (1, 2.5).
In general, if we want to find the solution to a linear equation in slope-intercept form, we can plug in any value of x that we want to find the corresponding value of y. This process is called graphing the line, and it is a useful way to visualize the solutions to linear equations.