To determine the equation of the line that passes through the points [tex]\((0, 6)\)[/tex] and [tex]\((-10, 0)\)[/tex], we need to follow these steps:
### Step 1: Calculate the Slope
The slope [tex]\(m\)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by the formula:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Substitute the coordinates of the given points:
[tex]\[ (x_1, y_1) = (0, 6) \][/tex]
[tex]\[ (x_2, y_2) = (-10, 0) \][/tex]
Now, calculate the slope:
[tex]\[ m = \frac{0 - 6}{-10 - 0} \][/tex]
[tex]\[ m = \frac{-6}{-10} \][/tex]
[tex]\[ m = 0.6 \][/tex]
### Step 2: Determine the Y-Intercept
The y-intercept [tex]\(b\)[/tex] of the line can be found using the equation of the line in slope-intercept form, [tex]\(y = mx + b\)[/tex]. Since we have already calculated the slope, we can use one of the points to find the y-intercept.
Using the point [tex]\((0, 6)\)[/tex]:
[tex]\[ y = mx + b \][/tex]
[tex]\[ 6 = 0.6 \cdot 0 + b \][/tex]
[tex]\[ b = 6 \][/tex]
### Step 3: Write the Equation of the Line
Now that we have both the slope [tex]\(m\)[/tex] and the y-intercept [tex]\(b\)[/tex], we can write the equation of the line:
[tex]\[ y = 0.6x + 6 \][/tex]
### Confirming Answer:
By comparing this equation with the given options, we see that the correct option is:
b. [tex]\( y = 0.6x + 6 \)[/tex]
Therefore, the best answer from the choices provided is:
B
