Final answer:
To find the equation of the line in slope-intercept form that passes through (-2, 8) and (-6, 0), calculate the slope as 2. Next, use either point to find the y-intercept as 12. The final equation is y = 2x + 12. So the y-intercept (b) is 12. The final equation of the line in slope-intercept form is y = 2x + 12.
Step-by-step explanation:
To write an equation of the line in slope-intercept form that passes through the two given points (-2, 8) and (-6, 0), we first need to find the slope (b) of the line. The slope is determined by the change in y divided by the change in x (rise over run). Using the given points:
- Slope, b = (y2 - y1) / (x2 - x1) = (0 - 8) / (-6 - (-2)) = (-8) / (-4) = 2
Now that we have the slope, we can use either one of the given points to find the y-intercept (a). Let's use the point (-2, 8) and the slope-intercept formula, which is y = mx + b, to solve for b.
- 8 = (2)(-2) + b
- 8 = -4 + b
- 12 = b
So the y-intercept (b) is 12. The final equation of the line in slope-intercept form is y = 2x + 12.