How to Draw a Line When an Equation is Given

 

How to Draw a Line When an Equation is Given

*A Step-by-Step Guide for Grade 7 Students*

Introduction:
In math, drawing a line from its equation helps us visualize relationships between variables. Today, we’ll learn how to plot a straight line using its equation. Let’s break it down into simple steps!

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Step 1: Understand the Equation

A common line equation is in the slope-intercept form:

$$y=mx+b$$

• $m$: Slope (how steep the line is).

• $b$: Y-intercept (where the line crosses the y-axis).

Example Equation:
Let’s use $y=2x+3$. Here, $m=2$ and $b=3$.

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Step 2: Plot the Y-Intercept

1. Look at $b$ in the equation. Here, $b=3$.

2. On graph paper, mark a point at $(0,3)$ on the y-axis.

 (Imagine a dot at (0,3)!)

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Step 3: Use the Slope to Find Another Point

• Slope ($m$) = $\frac{\text{Rise}}{\text{Run}}=\frac{2}{1}$ (since $2=\frac{2}{1}$).

  • Rise = 2: Move up 2 units.

  • Run = 1: Move right 1 unit.

Steps:

1. Start at the y-intercept $(0,3)$.

2. Move up 2 units → new y-coordinate: $3+2=5$.

3. Move right 1 unit → new x-coordinate: $0+1=1$.

4. Plot the second point at $(1,5)$.

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Step 4: Draw the Line

1. Place a ruler through the two points $(0,3)$ and $(1,5)$.

2. Extend the line in both directions and add arrows.

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Step 5: Verify with a Third Point (Optional)

To ensure accuracy, pick another $x$-value and find $y$:

• If $x=-1$:

  $$y=2(-1)+3=-2+3=1$$

  Plot $(-1,1)$—it should lie on the same line!

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Practice Problem

Try plotting the line for $y=-\frac{1}{2}x+4$:

1. Y-intercept: $(0,4)$.

2. Slope: Rise = $-1$, Run = $2$ (move down 1, right 2).

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Summary:

1. Start at $b$ (y-intercept).

2. Use $m$ to plot a second point.

3. Connect the dots and extend the line.

Video Explanation 

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How to Find the Midpoint

 

How to Find the Midpoint When Two Points Are Given

Definition:
The midpoint of a line segment is the point that is exactly in the middle of the two endpoints. It’s like the "average" of the two points.

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Formula to Find the Midpoint:

If you have two points on a graph:

• Point A: $(x_1,y_1)$

• Point B: $(x_2,y_2)$

The midpoint $M$ is calculated as:

$$M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$$

Steps:

1. Add the x-coordinates of the two points and divide by 2 → This gives the x-coordinate of the midpoint.

2. Add the y-coordinates of the two points and divide by 2 → This gives the y-coordinate of the midpoint.

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Examples:

Example 1: Simple Numbers

Points: $A(2,4)$ and $B(6,8)$Find the midpoint.

Solution:

1. x-coordinate of midpoint:

   $$\frac{2+6}{2}=\frac{8}{2}=4$$

2. y-coordinate of midpoint:

   $$\frac{4+8}{2}=\frac{12}{2}=6$$

3. Midpoint: $(4,6)$

Verification:

• The midpoint is exactly in the middle of (2,4) and (6,8).

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