Question

Write the point slope form of the equation of the line using the point (-4,-2)

Answer 1

Answer:

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

Step-by-step explanation:

1) First, find the slope of the line. Take two points the line intersects and use them for the slope formula, $\frac{y_2-y_1}{x_2-x_1}$. We already know the line intersects (-4, -2). Just choose any one of the points you can see the line intersecting (in this case, I chose (0,3)) and plug in its values, too. Then solve:

$\frac{(3)-(-2)}{(0)-(-4)} \\\frac{3+2}{0+4} \\\frac{5}{4}$

So, the slope is $\frac{5}{4}$.

2) Now that you have the slope, plug in values for the point-slope formula, $y - y_1 = m (x - x_1)$. In order to write a linear equation with it, the $x_1$, $y_1$, and $m$ have to be substituted for with real values. The $m$ represents the slope - which means that we should place $\frac{5}{4}$ there. The $x_1$ and $y_1$ represent the x and y values of a point - and the questions wants us to use (-4, -2), so substitute -4 for $x_1$ and -2 for $y_1$:

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

Thus, the answer is $y + 2 = \frac{5}{4} (x + 4)$.