Final answer:
The equation of the line in slope-intercept form that passes through the point (-8, 2) with a slope of 3 is y = 3x + 26.
Step-by-step explanation:
The student is asking for the equation of a line in slope-intercept form that passes through a specific point and has a given slope. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. To write the equation of the line, we can start by plugging the slope value and the coordinates of the given point into the formula to solve for b (the y-intercept).
Using the information provided, the slope (m) of the line is 3. Therefore, the slope-intercept form so far is y = 3x + b. Next, we can use the point (-8, 2) to find the y-intercept (b) by substituting -8 for x and 2 for y in the equation, which will give us 2 = 3(-8) + b. By solving this equation, we find that 2 = -24 + b and therefore, b = 26. Now we have both m and b, so the final slope-intercept form of the line is y = 3x + 26.