Question

Write an equation of the line that passes through the two points. $$(-3,-9),(5,7)$$

Short answer

The equation of a line that passes through the points (-3,-9) and (5,7) is \(y = 2x - 3\).

Step-by-step solution

Compute Slope of the Line

Firstly, you need to calculate the slope of the line that passes through the two points. You can use the slope formula, which is \(m = \frac{(y2 - y1)}{(x2 - x1)}\). With the given points being \((-3,-9),(5,7)\), let's plug them into the slope formula. This means you should have: \(m = \frac{(7 - (-9))}{(5 - (-3))}\).

Simplify the Slope

By simplification, \(m = \frac{16}{8}=2\). This tells us that the slope of the line is 2.

Find the Equation of the Line

Finally, we can use the point-slope form of a line equation that says \(y - y1 = m(x - x1)\), we can use any of two points but for this case, taking the point \((-3,-9)\), will insert this into the equation: \(y - (-9) = 2(x - (-3))\).

Simplify the Equation

The above equation simplifies to \(y + 9 = 2(x + 3)\). Distribute the 2 and then subtract 9 from both sides to get \(y = 2x + 6 - 9\). Thus the equation is \(y = 2x - 3\).