Answer:
Step-by-step explanation:
Question 1.
Slope of line 'l' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{8}{6}[/tex]
= [tex]\frac{4}{3}[/tex]
Equation of a line passing through (x', y') and slope 'm' is,
y - y' = m(x - x')
Since, line 'l' is passing through (0, 7) and slope = [tex]\frac{4}{3}[/tex]
Equation will be,
y - 7 = [tex]\frac{4}{3}(x-0)[/tex]
y = [tex]\frac{4}{3}x+7[/tex]
Similarly, slope of line m = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{-3}{6}[/tex]
= [tex]-\frac{1}{2}[/tex]
Therefore, equation of line 'm' passing through point (0, -4) will be,
y + 4 = [tex]-\frac{1}{2}(x - 0)[/tex]
y = [tex]-\frac{1}{2}x-4[/tex]
Solution = Point of intersection of both the lines
= (-6, -1)
Question 2
Slope of line 'l' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{-2}{5}[/tex]
Equation of line 'l' passing through a point (0, 4) and slope = -[tex]\frac{2}{5}[/tex]
y - 4 = [tex]-\frac{2}{5}(x-0)[/tex]
y = [tex]-\frac{2}{5}x+4[/tex]
Slope of line 'm' = [tex]\frac{\text{Rise}}{\text{Run}}[/tex]
= [tex]\frac{-2}{5}[/tex]
Equation of line 'm' passing through a point (0, -1) and slope = [tex]-\frac{2}{5}[/tex]
y + 1 = [tex]-\frac{2}{5}(x-0)[/tex]
y = [tex]-\frac{2}{5}x-1[/tex]
Since, slopes of both the lines are same, these lines will be parallel.
There will be NO SOLUTION.
