Questions: Find the slope-intercept form of the line that passes through (-6,10) and (2,-3) A. y=-16/5 x+17/5 B. y=16/5 x+17/5 C. y=13/8 x+1/4 D. y=-13/8 x+1/4

Solution Steps

To find the slope-intercept form of the line that passes through the points \((-6, 10)\) and \((2, -3)\), we need to:

1. Calculate the slope \(m\) using the formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
2. Use the point-slope form \(y - y_1 = m(x - x_1)\) to find the equation of the line.
3. Convert the equation to slope-intercept form \(y = mx + b\).

To find the slope \( m \) of the line passing through the points \((-6, 10)\) and \((2, -3)\), we use the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-3 - 10}{2 - (-6)} = \frac{-13}{8} = -1.625 \]

Next, we find the y-intercept \( b \) using the point-slope form of the equation. We can use one of the points, say \((-6, 10)\):

\[ b = y_1 - mx_1 = 10 - (-1.625)(-6) = 10 - 9.75 = 0.25 \]

Now that we have both the slope and the y-intercept, we can write the equation of the line in slope-intercept form:

\[ y = mx + b \implies y = -1.625x + 0.25 \]

Final Answer