Final answer:
The linear equation that has the solutions (2, 4) and (-2, 6) is found by calculating the slope from the points and then finding the y-intercept. The resulting equation is y = -1/2x + 5.
Step-by-step explanation:
To find the linear equation that has the solutions (2, 4) and (-2, 6), we need to determine the slope (m) and y-intercept (b) of a line that passes through these two points. The equation of a line in slope-intercept form is expressed as y = mx + b.
First, we calculate the slope using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the given points. So, the slope is (6 - 4) / (-2 - 2), which simplifies to 2 / -4 or -1/2.
Next, we use the slope and one of the points to find the y-intercept. Plugging the slope and point (2, 4) into the equation gives us:
4 = (-1/2)(2) + b
b = 4 + 1
b = 5
Therefore, the linear equation with the solutions (2, 4) and (-2, 6) is y = -1/2x + 5.