Marinaisom86idn
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Identify the zero of the line [tex]y + 5 = 5(x + 2)[/tex]. Then graph the line using the zero and the slope of the equation.

What is the zero of the line?

Type your answer as an ordered pair in the box.

The zero of the linear equation is [tex]\square[/tex].

To graph the equation, click on the Point button to place the two points on the graph. Do not use more than two points to graph the line. Additional points will be marked as incorrect.

Next, click on the Line button, then click on the two points you placed on the graph. This will draw the line between the points.

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- Line
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Sagot :

GinnyAnsweridn
Let's solve the linear equation step-by-step:

1. Rewrite the Given Equation: Start by writing the equation in a more familiar form. The given equation is:
[tex]\[ y + 5 = 5(x + 2) \][/tex]

2. Expand and Simplify: Distribute the 5 on the right side of the equation:
[tex]\[ y + 5 = 5x + 10 \][/tex]

3. Isolate [tex]\( y \)[/tex]: Subtract 5 from both sides to put the equation in the slope-intercept form [tex]\( y = mx + c \)[/tex]:
[tex]\[ y = 5x + 10 - 5 \][/tex]
[tex]\[ y = 5x + 5 \][/tex]

4. Find the Zero of the Line: The zero of the line (x-intercept) is where the line crosses the x-axis. To find this, set [tex]\( y = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[ 0 = 5x + 5 \][/tex]
[tex]\[ 5x = -5 \][/tex]
[tex]\[ x = -1 \][/tex]

Therefore, the zero of the line is:
[tex]\[ (-1, 0) \][/tex]

5. Determine the Slope: From the equation [tex]\( y = 5x + 5 \)[/tex], we see that the slope [tex]\( m \)[/tex] is 5.

6. Graphing the Line:
- First Point: The zero (x-intercept) we calculated, [tex]\((-1, 0)\)[/tex].
- Second Point: Use the slope [tex]\( m = 5 \)[/tex]. From the point [tex]\((-1, 0)\)[/tex], move up 5 units and to the right 1 unit to find the second point [tex]\((0, 5)\)[/tex].

These are the two points you need to plot on the graph to draw the line.

So, the final details are:

- The zero of the linear equation is [tex]\((-1, 0)\)[/tex].

To graph the line:
1. Place the first point at [tex]\((-1, 0)\)[/tex].
2. Place the second point at [tex]\((0, 5)\)[/tex].
3. Draw the line through these two points.

By following these steps, you will successfully identify the zero of the line and accurately graph the equation.
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