Final answer:
The student seeks the equation of a line through the point (–3, 2) with a negative slope. Options (c) and (d) are eliminated due to their positive slopes. Options (a) and (b) have the correct y-intercept and negative slopes, but additional data is needed to determine the exact equation.
Step-by-step explanation:
The student is asking for the equation of a line that passes through the point (–3, 2) and has a negative slope, since the line is described as 'sloping down and to the left'. The equation of a straight line is often written in the form y = mx + b, where m is the slope of the line and b is the y-intercept, which is the value of y when x=0. In this case, we know the line has a negative slope, but we don't have a precise value for the slope.
Examining the answer choices given, we can identify the slope and y-intercept:
- (a) –3x + 2 = y: Slope is -3 and y-intercept is 2.
- (b) –x + 2 = y: Slope is -1 and y-intercept is 2.
- (c) x – 3 = y: Slope is 1 (which is positive, so this can be eliminated) and y-intercept is -3.
- (d) 2x – 3 = y: Slope is 2 (which is positive, so this can be eliminated) and y-intercept is -3.
Since the line slopes down and to the left, we are looking for a negative slope; hence, options (c) and (d) can be ruled out because they have positive slopes. Among the remaining options, both (a) and (b) have negative slopes and intersect the y-axis at y=2. Without additional information such as the exact slope, we cannot definitively say which one is correct, but (a) and (b) remain possibilities.