Question

Write the equation of the line that passes through the points (4,-7) and (-3,5). Put your answer in fully reduced point slope-form, unless it’s a vertical or horizontal line

Answer 1

Step 1:

Write the given coordinates

(4 , -7) and (-3 , 5)

Step 2:

Write the two points equation of a line formula

$\frac{y-y_1}{x-x_1}\text{ = }\frac{y_2-y_1}{x_2-x_1}$

Step 3:

Write the data

$\begin{gathered} x_1\text{ = 4} \\ y_1\text{ = -7} \\ x_2\text{ = -3} \\ y_2\text{ = 5} \end{gathered}$

Step 4:

$\begin{gathered} \frac{y\text{ -(-7)}}{x\text{ - 4}}\text{ = }\frac{5\text{ -(-7)}}{-3\text{ - 4}} \\ \frac{y\text{ + 7}}{x\text{ - 4}}\text{ = }\frac{12}{-7} \\ \text{cross multiply} \\ -7(y\text{ + 7) = 12(x - 4)} \\ -7y\text{ - 49 = 12x - 48} \\ -7y=\text{ 12x - 48 + 49} \\ -7y\text{ = 12x + 1} \\ y\text{ = -}\frac{12}{7}x\text{ - }\frac{1}{7} \end{gathered}$

Final answer

$\text{Equation of a line is y = -}\frac{12}{7}x\text{ - }\frac{1}{7}$