Final answer:
To find the equation of the line with a y-intercept of 6 and passing through (10,10), calculate the slope as 0.4 and use the y-intercept to write the equation: y = 0.4x + 6.
Step-by-step explanation:
To determine the equation of a line with a y-intercept of 6 that passes through the point (10,10), we first need to find the slope of the line. The slope is calculated with the formula (change in y) / (change in x). Since we have the point (10, 10) and the y-intercept is at (0, 6), the slope (m) is (10 - 6) / (10 - 0) = 4 / 10 = 0.4. Now that we have the slope, we can use the y-intercept which is 6 (represented as 'b' in the equation), and the slope-intercept form of a line, which is y = mx + b, to write the equation of the line.
Plugging in the slope and y-intercept into the slope-intercept formula provides us with the equation of the line: y = 0.4x + 6.