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.
