A line on the coordinate grid can be defined by a slope-intercept equation: y = mx + b. For a given value of x, the value of y can be determined given the slope (m) and y-intercept (b) of the line. The slope of a line is change in y over change in x, \({\Delta y \over \Delta x}\), and the y-intercept is the y-coordinate where the line crosses the vertical y-axis.

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

b² - 6b + 9 = 0
(b - 3)(b - 3) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, (b - 3) must equal zero:

If (b - 3) = 0, b must equal 3

So the solution is that b = 3

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the equal sign and the answer on the other.

3z - 2 = 7 - z
3z = 7 - z + 2
3z + z = 7 + 2
4z = 9
z = \( \frac{9}{4} \)
z = 2\(\frac{1}{4}\)

An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite:

d° = b° + c°

To find angle c, remember that the sum of the interior angles of a triangle is 180°:

180° = a° + b° + c°
c° = 180° - a° - b°
c° = 180° - 39° - 53° = 88°

So, d° = 53° + 88° = 141°

A shortcut to get this answer is to remember that angles around a line add up to 180°:

a° + d° = 180°
d° = 180° - a°
d° = 180° - 39° = 141°

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 -1. 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, -4) and (2, 2) so the slope becomes:

Plugging these values into the slope-intercept equation:

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