Problemas
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.
Roztwór
Roberto
veterano · Tutor durante 11 años
4.3
(239 Votos)
Respuesta
To determine the relationship between Line A and Line B, we need to find the equations of both lines and then compare them.Step 1: Find the equation of Line A.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.First, let's find the slope of Line A using the given points (5,17) and (3,9).The formula for the slope is (y2 - y1) / (x2 - x1).Substituting the values, we get:m = (9 - 17) / (3 - 5) = -8 / -2 = 4Now that we have the slope, we can use one of the given points to find the y-intercept.Let's use the point (5,17).Substituting the values into the equation y = mx + b, we get:17 = 4(5) + b17 = 20 + bb = -3So, the equation of Line A is y = 4x - 3.Step 2: Find the equation of Line B.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).First, let's find the slope of Line B:m = (14 - (-6)) / (4 - (-1)) = 20 / 5 = 4Now, let's use one of the given points to find the y-intercept.Let's use the point (-1,-6).Substituting the values into the equation y = mx + b, we get:-6 = 4(-1) + b-6 = -4 + bb = -2So, the equation of Line B is y = 4x - 2.Step 3: Compare the equations of Line A and Line B.We can see that both lines have the same slope of 4. This means that they are parallel.Therefore, the correct statement is:Line A does not intersect line B.