Line A passes through the points (5,17) and (3,9) Line 8 passes through the points (-1,-6) and (4,14) Which statement is true? Line A does not intersect line B. Line A intersects line B at exactly one point. Line A overlaps line B.

To determine the relationship between Line A and Line B, we need to find the equations of both lines and then compare them.<br /><br />Step 1: Find the equation of Line A.<br />We can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope and b is the y-intercept.<br /><br />First, let's find the slope of Line A using the given points (5,17) and (3,9).<br />The formula for the slope is (y2 - y1) / (x2 - x1).<br />Substituting the values, we get:<br />m = (9 - 17) / (3 - 5) = -8 / -2 = 4<br /><br />Now that we have the slope, we can use one of the given points to find the y-intercept.<br />Let's use the point (5,17).<br />Substituting the values into the equation y = mx + b, we get:<br />17 = 4(5) + b<br />17 = 20 + b<br />b = -3<br /><br />So, the equation of Line A is y = 4x - 3.<br /><br />Step 2: Find the equation of Line B.<br />Using the same process as in Step 1, we can find the equation of Line B using the given points (-1,-6) and (4,14).<br /><br />First, let's find the slope of Line B:<br />m = (14 - (-6)) / (4 - (-1)) = 20 / 5 = 4<br /><br />Now, let's use one of the given points to find the y-intercept.<br />Let's use the point (-1,-6).<br />Substituting the values into the equation y = mx + b, we get:<br />-6 = 4(-1) + b<br />-6 = -4 + b<br />b = -2<br /><br />So, the equation of Line B is y = 4x - 2.<br /><br />Step 3: Compare the equations of Line A and Line B.<br />We can see that both lines have the same slope of 4. This means that they are parallel.<br /><br />Therefore, the correct statement is:<br />Line A does not intersect line B.