A linear equation has the general expression:
y=mx+b, where m is the slope of the line and b the intercept.
When two lines are parallel each other, this means that they have the same slope.
Line HC is represented by the formula: y=1*x+4, then it's slope equals 1, and it's intercept equals 4.
As mentioned, if line DQ is parallel to HC, then it's slope has to be equal to 1, let's write the formula of DQ with the information we have so far:
y=1*x+b,
Now, from the statement of the question, we know that line DQ goes through the point (1,0), which means that when x equals 1, y equals 0, let's replace this into the equation of line DQ and then solve for b.
y(1)=0=1*(1)+b, then:
b= -1
then the equation of line DQ is:
y=x-1, with an intercept of -1 and a slope of 1.