Question

Write the point-slope form of the equation of the line that passes through the two points. $$ (-3,-4),(1,-1) $$

Short answer

The equation of the line in point-slope form is \(y + 4 = \frac{3}{4}(x + 3)\).

Step-by-step solution

Calculate the Slope

Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Substitute the coordinates of the two given points into the formula: \(m = \frac{-1 - (-4)}{1 - (-3)} = \frac{3}{4}\).

Writing the Equation

Write the equation in point-slope form using the slope calculated in step 1 and the coordinates of one of the given points. For example, using the point (-3, -4), the equation becomes: \(y - (-4) = \frac{3}{4}(x - (-3))\)

Simplifying the Equation

Simplify the equation derived in Step 2 to its simplest form: \(y + 4 = \frac{3}{4}(x + 3)\). This is the equation of the line in point-slope form that passes through the given points.