To find the slope-intercept form of the equation that passes through the points \((-10, 3)\) and \((-5, 4)\), we first need to calculate the slope \(m\) using the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points \((-10, 3)\) \((x_1, y_1)\) and \((-5, 4)\) \((x_2, y_2)\):
\[ m = \frac{4 - 3}{-5 - (-10)} = \frac{1}{-5 + 10} = \frac{1}{5} \]
So the slope \(m\) is \(\frac{1}{5}\).
Next, we want to use the slope-intercept form of the equation, which is:
\[ y = mx + b \]
We already have \(m = \frac{1}{5}\). Now we can use one of the points to find \(b\). We can use either point; let's use \((-10, 3)\):
\[ 3 = \frac{1}{5}(-10) + b \]
Calculating this gives:
\[ 3 = -2 + b \]
Solving for \(b\):
\[ b = 3 + 2 = 5 \]
Thus, the equation in slope-intercept form is:
\[ y = \frac{1}{5}x + 5 \]
Now, let's check the options given:
A. \(y = 0.2x + 5\) (which is equivalent to \(y = \frac{1}{5}x + 5\))
B. \(y = 5x + 29\)
C. \(y = 0.2x + 3\)
D. \(y = 5x - 21\)
The only equation that matches our derived equation is option A: \(y = 0.2x + 5\).