Find the Line Equation Passing Through (0, -6) and (4, 0)

A straight line is drawn forming a triangle with the x and y axes.

The line passes through the points $(0,-6),(4,0)$ .

Choose the equation that represents the line.

Video Solution

Solution Steps

00:00 Find the algebraic representation of the line

00:03 We'll use the formula to find the slope of a line using 2 points

00:08 We'll substitute the points according to the given data and solve for the slope

00:29 This is the slope of the line

00:33 Now we'll use the slope of the line and a point on the line to find the equation

00:38 We'll use the line equation

00:42 We'll substitute appropriate values and solve to find the intersection point (B)

00:57 We'll isolate B

01:02 This is the intersection point of the line with the Y-axis

01:06 We'll substitute appropriate values and find the function

01:17 And this is the solution to the question

Step-by-Step Solution

Let's derive the equation of the line:

Step 1: Calculate the Slope
The slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is computed as follows: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points $(0, -6)$ and $(4, 0)$ : $m = \frac{0 - (-6)}{4 - 0} = \frac{6}{4} = \frac{3}{2}$ Hence, the slope of the line is $\frac{3}{2}$ .
Step 2: Write the Equation Using the Slope-Intercept Form
The slope-intercept form is: $y = mx + b$ Where $m$ is the slope and $b$ is the y-intercept. Since the line passes through $(0, -6)$ , this point is the y-intercept ( $b = -6$ ). Thus, we have: } $y = \frac{3}{2}x - 6$

Therefore, the equation of the line is $y = \frac{3}{2}x - 6$ .

The correct choice is option 4.