Question

Write the equation of a line Parallel to the given line and passes through points (-4, -3); (2, 3). Hints find the slope by using the slope formula and show your work in order to get credit!

Answer 1

First, we obtain the gradient (slope) of the first parallel line

`\text{gradient, m}_1\text{ = }(y_2-y_1)/(x_2-x_1)\text{ = }(3-(-3))/(2-(-4))=(6)/(6)\text{ = 1}`

Recall that since both lines are parallel, we have that,

`m_1=m_2`

Thus

`m_2\text{ = 1}`

Hence, we can find the equation of the parallel line given that it passes through the points (-4, -3)

Using

`\begin{gathered} y\text{ = mx + c} \\ \text{where m = m}_2\text{ = 1} \\ \text{and x = -4 , y = -3, we have} \\ -3\text{ = 1(-4) + c} \\ -3\text{ = -4 + c} \\ 4\text{ - 3 = c} \\ c\text{ = 1} \\ \text{Thus, the equation of the line is y = (1)x + 1} \\ y\text{ = x + 1} \end{gathered}`