A line passes through the points (1,1) and (2,7). Write its equation in slope-intercept form.

Sure, here are the steps to find the equation of the line in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept.

Step 1: Find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Here, (x1, y1) = (1, 1) and (x2, y2) = (2, 7).

m = (7 - 1) / (2 - 1) = 6 / 1 = 6

Step 2: Substitute the slope (m = 6) and one of the points into the equation y = mx + b to solve for b. Let's use the point (1, 1).

1 = 6*1 + b 1 = 6 + b b = 1 - 6 = -5

Step 3: Substitute m = 6 and b = -5 into the equation y = mx + b to get the final equation of the line.

y = 6x - 5

So, the equation of the line that passes through the points (1,1) and (2,7) in slope-intercept form is y = 6x - 5.