Line k goes through the points (–5, 3) and (–2, 1). Line m goes through the points (0, –3) and (2, 1). What is the point of intersection of lines k and m? A. (–1, 1) B. (1, –1) C. (1, 0) D. (2, 1)

To find the point of intersection of two lines, we first need to find the equations of the lines.

1. Find the slope of line k: The slope (m) is given by the formula m = (y2 - y1) / (x2 - x1) For line k, using the points (–5, 3) and (–2, 1), the slope is m = (1 - 3) / (-2 - (-5)) = -2 / 3 = -2/3

2. Find the equation of line k: The equation of a line is given by y = mx + b, where m is the slope and b is the y-intercept. To find b, substitute one of the points and the slope into the equation. Let's use the point (-5, 3). 3 = -2/3 * -5 + b 3 = 10/3 + b b = 3 - 10/3 = 9/3 - 10/3 = -1/3 So, the equation of line k is y = -2/3x - 1/3

3. Repeat steps 1 and 2 for line m: The slope of line m, using the points (0, -3) and (2, 1), is m = (1 - -3) / (2 - 0) = 4 / 2 = 2 To find b, substitute one of the points and the slope into the equation. Let's use the point (0, -3). -3 = 2 * 0 + b -3 = b So, the equation of line m is y = 2x - 3

4. Find the point of intersection: Set the two equations equal to each other and solve for x: -2/3x - 1/3 = 2x - 3 Multiply everything by 3 to get rid of the fractions: -2x - 1 = 6x - 9 Add 2x to both sides: -1 = 8x - 9 Add 9 to both sides: 8 = 8x Divide by 8: x = 1

5. Substitute x = 1 into either of the original equations to find y. Let's use y = 2x - 3: y = 2*1 - 3 = 2 - 3 = -1

So, the point of intersection of lines k and m is (1, -1), which corresponds to option B.