Final answer:
The equation of the line passing through the points (-8,-1) and (8,7) is y = 0.5x + 3. This was found by calculating the slope and then determining the y-intercept using one of the given points.
Step-by-step explanation:
The equation of the line that passes through the points (-8,-1) and (8,7) can be found by first calculating the slope of the line, and then using one of the points to find the y-intercept for the line equation in the slope-intercept form, which is y = mx + b, where 'm' is the slope and 'b' is the y-intercept.
To calculate the slope (m), use the formula m = (y2 - y1) / (x2 - x1), substituting in the values from the points (-8,-1) and (8,7). This gives us: m = (7 - (-1)) / (8 - (-8)) = 8/16 = 0.5.
Now, we choose one of the points to solve for the y-intercept (b) using the slope we calculated. Let's choose the point (8,7) and substitute into the line equation 7 = (0.5)(8) + b, which simplifies to 7 = 4 + b, and hence b = 3.
The final line equation in slope-intercept form is: y = 0.5x + 3.