Final answer:
The equation of the line passing through points (1,1) and (2,8) is y = 7x - 6, which is in slope-intercept form with a slope of 7 and a y-intercept of -6.
Step-by-step explanation:
To find the equation of the line in slope-intercept form given two points (1,1) and (2,8), we will first calculate the slope (m) of the line using the slope formula, which is the change in y divided by the change in x (m = (y2-y1)/(x2-x1)). Using our points, we get m = (8-1)/(2-1) = 7.
With the slope, we can then use the point-slope form of a line to find the equation. Since we know one point that lies on the line, the point (1,1), we can use it to find the y-intercept (b) of the equation. The point-slope form is given by y - y1 = m(x - x1). Substituting the known values gives us y - 1 = 7(x - 1). To convert this to slope-intercept form (y = mx + b), we expand to get y = 7x - 7 + 1, which simplifies to y = 7x - 6. Therefore, the equation of the line in slope-intercept form is y = 7x - 6, with a slope of 7 and a y-intercept of -6.