Final answer:
Line a and line b intersect at point (-2, -1).
Step-by-step explanation:
To determine if lines a and b intersect, we need to find their slopes. The formula to find the slope (m) of a line passing through two points (x1, y1) and (x2, y2) is: m = (y2 - y1) / (x2 - x1). For line a, using the points (0,4) and (1,7), the slope is: m = (7 - 4) / (1 - 0) = 3. For line b, using the points (2,1) and (6,4), the slope is: m = (4 - 1) / (6 - 2) = 0.75.
Since the slopes of lines a and b are different, they are not parallel. Therefore, lines a and b will intersect at a point. To find the point of intersection, we can set the equations of the lines equal to each other and solve for x and y.
Using the point-slope form of a line, the equation of line a is: y - 4 = 3(x - 0) which simplifies to y = 3x + 4. The equation of line b is: y - 1 = 0.75(x - 2) which simplifies to y = 0.75x + 0.5. Solving the system of equations, we find that lines a and b intersect at point (-2, -1).