Final answer:
To find the slope-intercept form of the line passing through the points (-2,4) and (2,6), calculate the slope as 0.5 and use it with one of the points to find the y-intercept, which is 5. The final equation is y = 0.5x + 5.
Step-by-step explanation:
The student is asking to find the slope-intercept form of the equation for a line that passes through two given points, (-2,4) and (2,6). To find the slope (m), we use the formula m = (y2 - y1) / (x2 - x1).
Thus, m = (6 - 4) / (2 - (-2))
= 2 / 4
= 0.5.
The slope is 0.5.
Next, we use one of the points and the slope to find the y-intercept (b).
Let's use (2,6). The equation for slope-intercept form is y = mx + b.
Plugging in the values, we get 6 = (0.5)(2) + b, which simplifies to 6 = 1 + b.
Hence, b = 6 - 1 = 5.
Therefore, the slope-intercept form of the equation for the line is y = 0.5x + 5.