Question

Write the system of equations shown on each graph, then give the solution to the system.

Answer 1

Answer:

Step-by-step explanation:

Question 1.

Slope of line 'l' = $\frac{\text{Rise}}{\text{Run}}$

                         = $\frac{8}{6}$

                         = $\frac{4}{3}$

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 = $\frac{4}{3}$

Equation will be,

y - 7 = $\frac{4}{3}(x-0)$

y = $\frac{4}{3}x+7$

Similarly, slope of line m = $\frac{\text{Rise}}{\text{Run}}$

                                         = $\frac{-3}{6}$

                                         = $-\frac{1}{2}$

Therefore, equation of line 'm' passing through point (0, -4) will be,

y + 4 = $-\frac{1}{2}(x - 0)$

y = $-\frac{1}{2}x-4$

Solution = Point of intersection of both the lines

               = (-6, -1)

Question 2

Slope of line 'l' = $\frac{\text{Rise}}{\text{Run}}$

                         = $\frac{-2}{5}$

Equation of line 'l' passing through a point (0, 4) and slope = -$\frac{2}{5}$

y - 4 = $-\frac{2}{5}(x-0)$

y = $-\frac{2}{5}x+4$

Slope of line 'm' = $\frac{\text{Rise}}{\text{Run}}$

                           = $\frac{-2}{5}$

Equation of line 'm' passing through a point (0, -1) and slope = $-\frac{2}{5}$

y + 1 = $-\frac{2}{5}(x-0)$

y = $-\frac{2}{5}x-1$

Since, slopes of both the lines are same, these lines will be parallel.

There will be NO SOLUTION.