To find the slope and y-intercept of the line given the points from the table, we first need to determine two points that we can use to calculate the slope. From the table, we can select two points: \((-5, 4)\) and \((10, -5)\).
Step 1: Calculate the slope (m)
The formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((-5, 4)\) and \((10, -5)\):
- \(x_1 = -5\), \(y_1 = 4\)
- \(x_2 = 10\), \(y_2 = -5\)
Substituting these values into the slope formula:
\[ m = \frac{-5 - 4}{10 - (-5)} = \frac{-9}{10 + 5} = \frac{-9}{15} = \frac{-3}{5} \]
Thus, the slope \(m\) is \(-\frac{3}{5}\).
Step 2: Find the y-intercept (b)
Next, we'll use the slope-intercept form of a line, which is given by:
\[ y = mx + b \]
We already have \(m = -\frac{3}{5}\). Now, we can use one of the points to find \(b\). Let's use the point \((0, 1)\) because it will provide the y-intercept directly if we substitute \(x = 0\):
Using the point \((0, 1)\) (where \(x = 0\), \(y = 1\)) to find \(b\):
\[ 1 = -\frac{3}{5}(0) + b \implies 1 = b \]
So, the y-intercept \(b\) is \(1\).
Step 3: Write the equation in slope-intercept form
Now, we can write the equation of the line using the values of \(m\) and \(b\):
\[ y = -\frac{3}{5}x + 1 \]
Conclusion
Thus, the slope of the line is \(-\frac{3}{5}\), the y-intercept is \(1\), and the equation of the line in slope-intercept form is:
\[ \boxed{y = -\frac{3}{5}x + 1} \]
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