To solve the equation [tex]\( y - 4 = 5(x + 1) \)[/tex] by finding and plotting two points, follow these steps:
1. Identify the equation in slope-intercept form:
- We start from the given equation: [tex]\( y - 4 = 5(x + 1) \)[/tex].
- Rearrange this equation to isolate [tex]\( y \)[/tex]:
[tex]\[
y - 4 = 5(x + 1)
\][/tex]
- Distribute the 5 on the right side:
[tex]\[
y - 4 = 5x + 5
\][/tex]
- Add 4 to both sides to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 5x + 9
\][/tex]
- This is now in the form [tex]\( y = mx + b \)[/tex] where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
2. Choose two values for [tex]\( x \)[/tex] to find corresponding points:
Let's choose [tex]\( x = 0 \)[/tex] and [tex]\( x = 1 \)[/tex].
- When [tex]\( x = 0 \)[/tex]:
[tex]\[
y = 5(0) + 9 = 9
\][/tex]
This gives the point [tex]\( (0, 9) \)[/tex].
- When [tex]\( x = 1 \)[/tex]:
[tex]\[
y = 5(1) + 9 = 14
\][/tex]
This gives the point [tex]\( (1, 14) \)[/tex].
3. Plot the points:
- The first point is [tex]\( (0, 9) \)[/tex].
- The second point is [tex]\( (1, 14) \)[/tex].
4. Draw the line:
- Plot these two points on the Cartesian plane and draw a line passing through both points. This line represents the equation [tex]\( y = 5x + 9 \)[/tex].
In summary, the two points you should plot are [tex]\( (0, 9) \)[/tex] and [tex]\( (1, 14) \)[/tex].
