find the equation of the line passes through the point (-1,2) and making an angle of 45° with the line x-y+1=0​

Step-by-step explanation:

line given is x-y+1= 0

you can rewrite it in slope intercept y=mx+b where m is the slope, and b is the y-intercept where the line meets the y-axis

x-y+1 =0 subtract x and 1 from both sides of the equation

-y = -x-1 multiply both sides by -1

y = x+1 so the slope of this line is 1 and the y-intercept is 1

If you draw this line you can see that there are actually 2 lines that form 45° angles with y=x+1 and pass through (-1, 2), one is vertical x= -1 and one horizontal y =2