Tutor profile: Cheryl D.

Find the length of the diagonal of a square with side length = 4.

Draw a square and a diagonal. The diagonal forms two right, issociles triangles with side lengths = 4. Use the Pythagorean theorem or special right triangles to solve. Pythagorean theorem: 4^2 + 4^2 = c^2 (c is the diagonal which is the hypotenuse) So 32 = c^2 and c = sq. root of 32 = 5.66. Special right triangles:

Find the slope of the line through points through: (−4, 0) and (1, 5)

Take the difference of the y coordinates 0 and 5 and that will be the numerator. Take the difference of the x coordinates -4 and 1 and that will be the denominator. So, you have: -5 / -5. (That's -5 over -5) = 1. So the slope = 1.

Write the slope-intercept form of the equation of the line through the point (0, 3) and (−4, −1).

First find the slope of the line using the given points. Do this by finding the change in the y coordinates and divide by the change in the x coordinates. Or, Y2-Y1 / X2-X1. So (-1 - 3) / (-4 - 0). So -4 / -4 = 1. Slope (m) = 1. Next, find the y intercept using y=mx+b and one of the given points, say (0,3). Fill in the known variables into y=mx+b and solve for b. So, 3 = 1(0) + b so 3 = 0+b and 3= b. Last, write your equation in y=mx+b form so y = 1x + 3.