Line A passes through the points (-2,27) and (1,-9). Line B passes through the points (-1,15) and (3,-33). Which statement is true? Choices: (A)Line A does not intersect line B. (B)Line A overlaps line B. (C)Line A intersects line B at exactly one point.

Calculate Slope Line A: Calculate the slope of Line A using the points (-2,27) and (1,-9). Slope formula: m = (y2 - y1) / (x2 - x1) m = (-9 - 27) / (1 - (-2)) m = (-36) / 3 m = -12 Calculate Slope Line B: Calculate the slope of Line B using the points (-1,15) and (3,-33). Slope formula: m = (y2 - y1) / (x2 - x1) m = (-33 - 15) / (3 - (-1)) m = (-48) / 4 m = -12 Compare Slopes: Compare the slopes of Line A and Line B. Both Line A and Line B have the same slope, m = -12. Since the slopes are equal, the lines are either parallel or overlapping. Check Y-Intercepts: Check if Line A and Line B are the same line by finding the y-intercept of each line. For Line A, using point (-2,27) and slope -12: y - y1 = m(x - x1) 27 - (-12)(-2 - x) 27 = -12x - 24 51 = -12x x = -51/12 This calculation is incorrect; we should be finding y-intercept (b), not x.

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Line A passes through the points $(-2,27)$ and $(1,-9)$ . Line B passes through the points $(-1,15)$ and $(3,-33)$ . Which statement is true? $\newline$ Choices: $\newline$ (A) Line A does not intersect line B. $\newline$ (B) Line A overlaps line B. $\newline$ (C) Line A intersects line B at exactly one point.

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Math Problems

Algebra 2

Write a quadratic function from its vertex and another point

Full solution

Q. Line A passes through the points

(-2,27)

and

(1,-9)

. Line B passes through the points

(-1,15)

and

(3,-33)

. Which statement is true?

\newline

Choices:

\newline

(A) Line A does not intersect line B.

\newline

(B) Line A overlaps line B.

\newline

Calculate Slope Line A: Calculate the slope of Line A using the points $(-2,27)$ and $(1,-9)$ . $\newline$ Slope formula: $m = \frac{(y_2 - y_1)}{(x_2 - x_1)}$ $\newline$ $m = \frac{(-9 - 27)}{(1 - (-2))}$ $\newline$ $m = \frac{(-36)}{3}$ $\newline$ $m = -12$
Calculate Slope Line B: Calculate the slope of Line B using the points $(-1,15)$ and $(3,-33)$ . $\newline$ Slope formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ $\newline$ $m = \frac{-33 - 15}{3 - (-1)}$ $\newline$ $m = \frac{-48}{4}$ $\newline$ $m = -12$
Compare Slopes: Compare the slopes of Line A and Line B. $\newline$ Both Line A and Line B have the same slope, $m = -12$ . $\newline$ Since the slopes are equal, the lines are either parallel or overlapping.
Check Y-Intercepts: Check if Line A and Line B are the same line by finding the y-intercept of each line. $\newline$ For Line A, using point $(-2,27)$ and slope $-12$ : $\newline$ $y - y_1 = m(x - x_1)$ $\newline$ $27 - (-12)(-2 - x)$ $\newline$ $27 = -12x - 24$ $\newline$ $51 = -12x$ $\newline$ $x = -\frac{51}{12}$ $\newline$ This calculation is incorrect; we should be finding y-intercept $b$ , not $x$ .