Question

Write an equation in slope-intercept form of the line that passes through the points. $$ (-8,9),(10,-3) $$

Short answer

The equation of the line in slope-intercept form that passes through the points (-8,9) and (10,-3) is \( y = -2/3x + 5 \).

Step-by-step solution

Identify the Given Points

The points given in this problem are (-8,9) and (10,-3). Thus, we can identify x1 = -8, y1 = 9, x2 = 10, and y2 = -3.

Calculate the Slope

Next, we can calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Substituting the known values, we get m = (-3 - 9) / (10 - (-8)) = -12 / 18 = -2/3.

Calculate the y-intercept

Using the equation y - y1 = m(x - x1), we substitute the values of the slope and one of the points, say (-8,9), into the equation to calculate the y-intercept. This gives us y - 9 = -2/3(x - (-8)). Simplifying, we find y = -2/3x + 5.