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

00:11 Let's find the algebraic formula for this line.

00:14 We'll use the slope formula with two points. Are you ready?

00:19 Now, substitute the points from the data to find the slope. Let's solve it.

00:40 Great job! This is the slope of the line.

00:44 Next, we'll use the slope and a point to find the line's equation.

00:49 We'll apply the line equation now. Are you following along?

00:53 Let's substitute the values to find the Y-intercept, B.

01:08 Now, let's solve to isolate B.

01:13 Well done! This is where the line intersects the Y-axis.

01:17 Let's plug in the values and find the function.

01:28 And there you have it! That's the solution to our problem.

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.