A line L is parallel to y=4x+5 and passes through the point (-1, 6). Find the equation of the line L in the form y=ax+b . Find also the coordinates of its intersections with the axes.

Since L is parallel to y=4x+5 we know that the two lines have the same gradient. The gradient of a line in the form y=ax+b has is a, which means the gradient of y=4x+5 is 4, so L is y=4x+b and we just need to find b. L passes through the point (-1,6) so this point must satisfy the equation. Substituting the point into y=4x+b gives 6=4(-1)+b, which we can rearrange to give b=10. So we've found the equation for L: y=4x+10. Now to find where L intersects the axes, starting with the y-axis. The x-coordinate of any point on the y-axis is 0, so to find the y-coordinate we can plug x=0 into the equation to give y=4(0)+10=10. So L crosses the y-axis at the point (0,10). Similarly, we can find the x-coordinate of the intersection with the x-axis by taking y=0 and substituting this into the equation, giving 0=4x+10, so 4x=-10, and x=-10/4. So L crosses the x-axis at (-10/4,0).