Final answer:
The graph of the function -14x + 35y = -28 is a straight line with a negative slope, meaning it slopes downward to the right. The equation rewritten in the form y = -2/5x - 4/5 confirms it is a line, as per the slope-intercept form of linear equations.
Step-by-step explanation:
The question asks about the graph of a function, specifically the function -14x + 35y = -28. To determine what the graph looks like, we can rearrange the equation into slope-intercept form (y = mx + b), which is the standard form for the equation of a straight line. Doing so, we add 14x to both sides and divide everything by 35 to isolate y, resulting in y = -2/5x - 4/5. This shows that the graph is indeed a straight line with a negative slope, indicating that it slopes downward to the right. According to the options provided, the correct answer is (b) A Line.
Figure 12.4 in the reference material affirms that, given a linear equation of the form y = a + bx, the graph is a straight line. The coefficient b determines the slope of the line, and in this case, since b is negative (-2/5), the line slopes downward to the right. The reference material also emphasizes that the slope is constant along the entire length of the line and that a change in the value of x will consistently result in a proportional change in the value of y, as per the slope.