Final answer:
Given a line with y-intercept (0,-12) and slope 4/5, the line's point of intersection with the x-axis is found by setting y to 0 in the line's equation, and solving for x. This results in the intersection point being (15,0).
Step-by-step explanation:
Given that the line has a y-intercept of (0,-12) and a slope of (4/5), we are tasked with finding the point of intersection of this line with the x-axis. First, let's understand that a line intersects the x-axis where the y-value is zero. Hence, we can set the y-value to zero in the line's equation.
The line's equation would be given as y = mx + b, where 'm' is the slope and 'b' is the y-intercept. In our case, the equation of the line becomes y = (4/5)x - 12. Setting y = 0, we get: 0 = (4/5)x - 12.
Solving for x, we add 12 to both sides, getting (4/5)x = 12. Then, we multiply both sides by 5/4, yielding x = 15. So, the line intersects the x-axis at the point (15,0).
Learn more about Line Intersection