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

Q: How do I remember which coordinate goes where in the slope formula?

Remember "y over x" - the y-coordinates go in the numerator, x-coordinates in the denominator. Think of slope as "rise over run" where rise is vertical (y-direction) and run is horizontal (x-direction).

Q: Can I use the other point (4, 0) to find the equation?

Yes! You can use either point with point-slope form: $ y - 0 = \frac{3}{2}(x - 4) $. When you simplify, you'll get the same answer: $ y = \frac{3}{2}x - 6 $.

Q: Why is the y-intercept -6 and not 6?

The y-intercept is the y-coordinate when x = 0. Looking at point (0, -6), the y-value is negative 6, so b = -6. Don't drop the negative sign!

Q: How can I double-check my final equation?

Substitute both given points into your equation. For $ y = \frac{3}{2}x - 6 $:Point (0, -6): $ -6 = \frac{3}{2}(0) - 6 = -6 $ ✓Point (4, 0): $ 0 = \frac{3}{2}(4) - 6 = 0 $ ✓

Linear Equations with Point-Slope Method

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.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

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.

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.

Final Answer

$y=\frac{3}{2}x-6$

Key Points to Remember

Essential concepts to master this topic

Slope Formula: Use $m = \frac{y_2 - y_1}{x_2 - x_1}$ to find rise over run
Y-intercept: Point (0, -6) directly gives b = -6 in y = mx + b
Verification: Substitute both points: $\frac{3}{2}(4) - 6 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Confusing x and y coordinates when calculating slope
Don't switch coordinates like $\frac{4-0}{0-(-6)} = \frac{4}{6}$ = wrong slope! This gives you the reciprocal and leads to equations like y = 2/3x - 6. Always use $\frac{y_2-y_1}{x_2-x_1}$ in the correct order.

Practice Quiz

Test your knowledge with interactive questions

Which statement best describes the graph below?

FAQ

Everything you need to know about this question

How do I remember which coordinate goes where in the slope formula?

Remember "y over x" - the y-coordinates go in the numerator, x-coordinates in the denominator. Think of slope as "rise over run" where rise is vertical (y-direction) and run is horizontal (x-direction).

What if I get a negative slope instead of positive?

Check your coordinate subtraction! With points (0, -6) and (4, 0), you should get $\frac{0-(-6)}{4-0} = \frac{6}{4}$ . If you got negative, you likely forgot that subtracting a negative gives positive.

Can I use the other point (4, 0) to find the equation?

Yes! You can use either point with point-slope form: $y - 0 = \frac{3}{2}(x - 4)$ . When you simplify, you'll get the same answer: $y = \frac{3}{2}x - 6$ .

Why is the y-intercept -6 and not 6?

The y-intercept is the y-coordinate when x = 0. Looking at point (0, -6), the y-value is negative 6, so b = -6. Don't drop the negative sign!

How can I double-check my final equation?

Substitute both given points into your equation. For $y = \frac{3}{2}x - 6$ :

Point (0, -6): $-6 = \frac{3}{2}(0) - 6 = -6$ ✓
Point (4, 0): $0 = \frac{3}{2}(4) - 6 = 0$ ✓

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