Final answer:
To find the point of intersection between two lines, solve the system of equations formed by the lines. Substitute the solution into one of the original equations to find the coordinates of the intersection point.
Step-by-step explanation:
To find the point at which two lines intersect, we need to solve the system of equations formed by the two lines. Let's assume we have two lines in slope-intercept form, y = mx + b. We equate the two equations and solve for x and y to find the intersection point. The coordinates of the intersection point will be the solution to the system of equations.
For example, if we have the lines y = 2x + 5 and y = -3x + 7, we can set them equal to each other: 2x + 5 = -3x + 7. Solving this equation will give us the x-coordinate of the intersection point. Substituting this value back into one of the original equations will give us the y-coordinate.
In this case, solving the equation 2x + 5 = -3x + 7 gives us x = 1. Plugging this value into either equation, we find y = 2(1) + 5 = 7. Therefore, the intersection point is (1, 7).