The slope of all parallel lines are equal.
The slope of a line in the form [tex]y=mx+c[/tex] is m.
1. The given equation is: [tex]y=4x+2[/tex]. The slope of this line is [tex]m=4[/tex]. The slope of the line parallel to this line is also 4.
2. The given equation is [tex]y=\frac{2}{7}x+1[/tex]. The slope of this line is [tex]m=\frac{2}{7}[/tex].
The slope of the line parallel to it is also [tex]\frac{2}{7}[/tex].
3. The next equation is [tex]y+9x=13[/tex]. The slope intercept form is [tex]y=-9x+13[/tex].
The slope of this is [tex]m=-13[/tex]. The line parallel to it also has slope which is -13.
4. The given equation is [tex]y=-\frac{1}{2}x+4[/tex]. The slope of this line and the line parallel to it is [tex]m=-\frac{1}{2}[/tex]
5. The equation is 6x+2y=4. We simplify to get: 3x+y=2.
The slope-intercept form is [tex]y=-3x+2[/tex]. The line parallel to this line has slope [tex]m=-3[/tex]
6. Assuming the line is [tex]y=-3x+9[/tex], then the slope is [tex]m=-3[/tex]
7. Assuming the line is [tex]-5x+5y=4[/tex], then the slope-intercept form is [tex]y=x+\frac{4}{5}[/tex] and the slope of the line parallel to this line is m=1
8. The equation is 9x-5y=4. The slope intercept form is [tex]y=\frac{5}{9}x-\frac{4}{9}[/tex]. The slope of the line parallel to this line is [tex]m=\frac{5}{9}[/tex]
9. The given equation is [tex]-x+3y=6[/tex]. The slope intercept form is [tex]y=\frac{1}{3}x+2[/tex]. The line parallel to this line also has slope[tex]m=\frac{1}{3}[/tex].
10. Assuming the given line is 6x-7y=10, then [tex]y=\frac{6}{7}x-\frac{10}{7}[/tex] and the line parallel to it has slope [tex]m=\frac{6}{7}[/tex]
11. Assuming the line is [tex]y-x=-3[/tex], then [tex]y=x-3[/tex] and the slope of the line parallel to it is [tex]m=1[/tex]
12. The given line is 3x-5y=6. This implies that [tex]y=\frac{3}{5}x-\frac{6}{5}[/tex]
