Final answer:
To find the x-coordinate of intersection between a line and a perpendicular line, we set the equations equal to each other and solve for x. In this case, the lines intersect at x = 8.
Step-by-step explanation:
To find the x-coordinate at which a line with the equation y = 2x - 3 intersects a perpendicular line with a y-intercept of 17, we can set the two equations equal to each other and solve for x.
The equation of the perpendicular line can be written as y = mx + b, where m is the slope and b is the y-intercept.
Since two lines are perpendicular if and only if their slopes are negative reciprocals of each other, the slope of the perpendicular line would be -1/2.
The equation of the perpendicular line becomes y = (-1/2)x + 17.
Setting the two equations equal to each other, we have 2x - 3 = (-1/2)x + 17. Solving for x, we get 2.5x = 20, which simplifies to x = 8. Therefore, the two lines intersect at x = 8.