Find the equation of a line that passes through the point (-2, 5) and makes an angle of 45° with the positive part of the -axis

Hello!

You haven't specified which axis to consider, x or y, but luckily for the angle of 45 degrees it isn't important:)

But there are still two such lines, one goes 45 degrees up to the right, another goes 45 degrees down.

For the first line, the slope is tan(45°)=1, and the equation is in the form y=x+b. The point (x=-2, y=5) must satisfy this equation, so 5=-2+b and b=7. The final equation is y=x+7.

For the second line, the slope is tan(-45°)=-1, and the equation is y=-x+d, 5=-(-2)+d, so d=3 and the equation is y=-x+3.