This question tests graph interpretation, requiring the slope from a line equation in standard form. To find the slope, rewrite 2x + 5y = 10 as y = -2/5 x + 2, where -2/5 is the slope. This form highlights the negative slope and y-intercept of 2. Applying the conversion confirms the slope as -2/5. Thus, the correct answer is -2/5, choice A. A common incorrect option is -5/2, from swapping numerator and denominator. Another mistake could be forgetting the negative sign, leading to 2/5.

This question tests coordinate geometry, specifically identifying the y-intercept from a line equation. In the equation y = -1/3x + 4, which is in slope-intercept form y = mx + b, the constant term b represents the y-intercept. The y-intercept is 4, which is the y-value when x = 0: y = -1/3(0) + 4 = 4. This means the line crosses the y-axis at the point (0,4). Students often confuse the slope (-1/3) with the y-intercept or mistakenly write the y-intercept as a coordinate pair like (4,0).

This question tests graph interpretation, applying a horizontal shift to the line y = -3/2 x + 6. Shifting right by 2 replaces x with (x-2), yielding y = -3/2 (x-2) + 6. This maintains the slope but adjusts the intercept. Expanding gives y = -3/2 x + 9, equivalent to the form in C. Therefore, Choice C is correct. A common mistake is shifting left, leading to (x+2). Another error could be vertical shift confusion, altering the constant incorrectly.

This question tests graph interpretation, specifically finding the y-intercept from a linear equation in standard form. The y-intercept occurs where the line crosses the y-axis, which is when x = 0. Substituting x = 0 into 3x + 2y = 12 gives: 3(0) + 2y = 12, so 2y = 12, and y = 6. Therefore, the y-intercept is 6, or the point (0,6). A common mistake is confusing the y-intercept with the x-intercept (which would be 4) or misidentifying coefficients as intercepts.

This question tests graph interpretation, comparing slopes and intercepts to determine line relationships. Both lines have slope 3/4 but different y-intercepts (1 and -5), indicating they are parallel and distinct. Parallel lines never intersect and maintain constant distance. This relationship is confirmed by the identical slopes and unequal intercepts. Thus, Choice C is correct. A common mistake is assuming they intersect at one point due to similar slopes. Another error could be thinking they are the same line if intercepts are miscompared.

This question tests graph interpretation, specifically understanding vertical translations of linear functions. The original line y = x - 4 has y-intercept -4 (when x = 0, y = -4). When a line is shifted upward by 6 units, we add 6 to the entire equation: y = x - 4 + 6 = x + 2. The new line has equation y = x + 2, so its y-intercept is 2. This vertical shift moves every point on the line up by 6 units, including the y-intercept which moves from -4 to 2. A common error is subtracting instead of adding the shift amount.

This question tests graph interpretation, specifically identifying the y-intercept from a line equation in slope-intercept form. The equation y = 3x - 7 is already in the form y = mx + b, where b is the y-intercept. The y-intercept occurs when x = 0, giving y = 3(0) - 7 = -7. Therefore, the y-intercept is -7, which represents the point where the line crosses the y-axis. A common mistake is confusing the slope (3) with the y-intercept or misidentifying the sign, thinking the y-intercept is positive 7.

This question tests graph interpretation, calculating slope from x- and y-intercepts. The points (0,-2) and (5,0) give slope m = (0 - (-2))/(5 - 0) = 2/5. This positive slope shows the line rising from left to right. Applying the formula confirms this value. Therefore, Choice A is correct. A common incorrect option is -2/5, from neglecting the double negative. Another mistake might be inverting to 5/2.

This question tests graph interpretation, specifically identifying the slope from a line equation in slope-intercept form. The equation y = -4x + 9 follows the pattern y = mx + b, where m is the slope and b is the y-intercept. The coefficient of x is -4, so the slope is -4. This means the line decreases by 4 units vertically for every 1 unit increase horizontally. A common error is confusing the slope with the y-intercept (9) or misreading the negative sign, leading to answers like 4 or 9/4.

This question tests graph interpretation, focusing on identifying the y-intercept from a line's equation in slope-intercept form. The y-intercept is the value of y where the line crosses the y-axis, represented by the constant term b in y = mx + b. For the equation y = 3x - 7, the slope m is 3, and the y-intercept b is -7. This directly gives the y-intercept as -7. Therefore, the correct answer is -7, which is choice B. A common mistake is confusing the y-intercept with the slope, leading to selecting 3. Another error might involve misreading the sign, resulting in choices like 7.