To graph the equation [tex]\( y + 6 = \frac{4}{5}(x + 3) \)[/tex], we will transform it into the slope-intercept form [tex]\( y = mx + b \)[/tex] and identify its slope and y-intercept.
1. Start with the given equation:
[tex]\[ y + 6 = \frac{4}{5}(x + 3) \][/tex]
2. Distribute the fraction on the right-hand side:
[tex]\[ y + 6 = \frac{4}{5}x + \frac{4}{5} \times 3 \][/tex]
[tex]\[ y + 6 = \frac{4}{5}x + \frac{12}{5} \][/tex]
3. Isolate [tex]\( y \)[/tex] by subtracting 6 from both sides:
[tex]\[ y = \frac{4}{5}x + \frac{12}{5} - 6 \][/tex]
4. Convert 6 into a fraction with a denominator of 5 to combine the fractions:
[tex]\[ 6 = \frac{30}{5} \][/tex]
[tex]\[ y = \frac{4}{5}x + \frac{12}{5} - \frac{30}{5} \][/tex]
5. Combine the terms:
[tex]\[ y = \frac{4}{5}x - \frac{18}{5} \][/tex]
So, the slope-intercept form of the equation is:
[tex]\[ y = \frac{4}{5}x - \frac{18}{5} \][/tex]
Here:
- The slope [tex]\( m \)[/tex] is [tex]\( \frac{4}{5} \)[/tex] or 0.8
- The y-intercept [tex]\( b \)[/tex] is [tex]\( -\frac{18}{5} \)[/tex] or -3.6
Next, we need two points to graph the line:
- The y-intercept itself is a point: [tex]\((0, -3.6)\)[/tex]
Let's choose another point by selecting [tex]\( x = 5 \)[/tex]:
\- Substitute [tex]\( x = 5 \)[/tex] into the equation:
[tex]\[ y = \frac{4}{5}(5) - \frac{18}{5} \][/tex]
[tex]\[ y = 4 - \frac{18}{5} \][/tex]
[tex]\[ y = 4 - 3.6 \][/tex]
[tex]\[ y = 0.4 \][/tex]
So, the coordinates of the second point are [tex]\((5, 0.4)\)[/tex].
In conclusion:
- The slope is 0.8.
- The y-intercept is -3.6.
- Two points on the line are [tex]\((0, -3.6)\)[/tex] and [tex]\((5, 0.4)\)[/tex].
You can now use these points to graph the line. Select the line tool and plot the points:
1. Start at [tex]\((0, -3.6)\)[/tex]
2. Move to [tex]\((5, 0.4)\)[/tex]
Draw the line through these points to graph the equation.
