Final answer:
The statement that the equation y = -5x - 4 passes through the point (3, -18) is false. When substituting x = 3 into the equation, it yields y = -19, which does not match the y-value of the point in question.
Step-by-step explanation:
The equation given is y = -5x - 4, which represents a straight line. To determine if this line passes through the point (3, -18), you can substitute the x value from the point into the equation and see if the corresponding y value fits. By plugging in x = 3, the equation would yield y = -5(3) - 4, which simplifies to y = -15 - 4, and further to y = -19. Since this result (-19) does not equal the y value of the point (-18), the statement is false.
To understand this concept further, let's take a look at linear equations in general. A linear equation will always graph as a straight line. The form y = mx + b is called the slope-intercept form where 'm' represents the slope and 'b' is the y-intercept. If a line has a positive slope, this means that as x increases, y increases. Conversely, a negative slope means that as x increases, y decreases. In the case of the equation y = -5x - 4, the slope is -5, which indicates a line that slopes downward from left to right.
Looking at the other references, for example, the line of best fit y = -173.5 + 4.83x has a positive slope, implying the line goes upward as x increases, directly opposing our initial negative-sloped line. Furthermore, when the slope of the line is positive and the y-intercept is a positive value, as stated in another reference, the line will also ascend on the graph. Remember, the slope is constant for a linear equation, which means that the line does not curve but rather maintains the same incline or decline throughout.