The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -2. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, -3) and (2, -1) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = \(\frac{1}{2}\)x - 2

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)

To factor a quadratic expression, apply the FOIL (First, Outside, Inside, Last) method in reverse.

To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.

5a + 2a = 7a

The surface area of a cylinder is 2πr² + 2πrh:

sa = 2πr² + 2πrh
sa = 2π(7²) + 2π(7 x 5)
sa = 2π(49) + 2π(35)
sa = (2 x 49)π + (2 x 35)π
sa = 98π + 70π
sa = 168π