To determine which of the provided options represents the line that passes through the points (-1, 10) and (3, 2), we first need to find the equation of this line.
-
Calculate the slope (m): The formula for the slope between two points \((x_1, y_1)\) and \((x_2, y_2)\) is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the given points (-1, 10) and (3, 2): \[ m = \frac{2 - 10}{3 - (-1)} = \frac{-8}{4} = -2 \]
-
Find the y-intercept (b): We can use the slope-intercept form of the line: \[ y = mx + b \] We can use one of the points to solve for \(b\). Let's use the point (-1, 10): \[ 10 = -2(-1) + b \implies 10 = 2 + b \implies b = 10 - 2 = 8 \]
-
Write the equation of the line: Combining the slope and y-intercept, the equation of the line is: \[ y = -2x + 8 \]
-
Identifying points on the line: To draw this line accurately, we can identify a few points:
- If \(x = 0\), then \(y = 8\) → Point (0, 8)
- If \(x = 4\), then \(y = 0\) → Point (4, 0)
Now, let's compare this with the provided options:
- The first option indicates a line going through points (0, 8) and (4, 0), which matches our derived points.
- The second option doesn’t match the slope or any known points.
- The third option indicates a line going through points that don't match.
- The fourth option also does not match our line.
Therefore, the line that passes through the points (-1, 10) and (3, 2) corresponds to the first option: On a coordinate plane, a line goes through points (0, 8) and (4, 0).