Question

Give the equation of the line passing through the points (-4, 14) and(3,-3).Pls see picture

Answer 1

We need to determine the equation for the line that passes through the two points:

$\begin{gathered} (-4,14) \\ (3,-\frac{7}{2}) \end{gathered}$

For that we need to determine the slope for the line, which is given by:

$m=\frac{y_2-y_1}{x_2-x_1}$

Where m is the slope, (x1, y1) and (x2, y2) are the coordinates of the two points.

$\begin{gathered} m=\frac{14-(-\frac{7}{2})}{-4-3} \\ m=\frac{14+\frac{7}{2}}{-7} \\ m=\frac{\frac{35}{2}}{-7} \\ m=-\frac{35}{14} \end{gathered}$

Now we need to use one of the points to determine the full equation, as shown below:

$y-y_1=m\cdot(x-x_1)$

Where (x1, y1) are the coordinates of one of the points.

$y-14=\frac{-35}{14}(x+4)$

Now we need to isolate the y-variable on the left side.

$\begin{gathered} y=\frac{-35}{14}x-\frac{35}{14}\cdot4+14 \\ y=\frac{-35}{14}x+4 \end{gathered}$

The equation for the line is y = -35x/14 + 4