I am helping my son to understand the correct process for two math examples:
*If the line with equation 3x-4ky= -16 has y-intercept -2, find k.
*Write the equation of the line passing through (2,5) and perpendicular to the line passing through (2,-4) and (6,1)
Your help in assisting us would be greatly appreciated.
The y-intercept is the y-coordinate of the point where the line crosses the y-axis. Since this is a point on the y-axis, the x-coordinate is zero. In your first problem the y-intercept is -2 and hence the point where the line crosses the y-axis is (0,-2).
Since (0,-2) is on the line, (0,-2) satisfies the equation of the line. Thus
The fact that you need to solve the second problem is that the products of the slopes of two perpendicular lines is -1. The line through (2,-4) and (6,1) has slope
Finally write the equation of the line through (2,5) with slope -4/5Cheers,