The equation representing the straight line passing through the points (4, 8) and (-6, 2) is y = 1/2 * x + 5.
To find the equation of a straight line, we can use the slope-intercept form, which is given by y = mx + b, where m is the slope and b is the y-intercept. The slope (m) can be found using the formula m = (y₂ - y₁) / (x₂ - x₁), where (x₁, y₁) and (x₂, y₂) are two points on the line.
In this case, the given points are (4, 8) and (-6, 2). Substituting these values into the slope formula, we get m = (2 - 8) / (-6 - 4) = 1/2. Now that we have the slope, we can use one of the points (let's use (4, 8)) to find the y-intercept (b). Substituting the values into the slope-intercept form, we get 8 = 1/2 * 4 + b, which simplifies to b = 5.
Therefore, the equation of the straight line is y = 1/2 * x + 5. This equation represents a line with a slope of 1/2 and a y-intercept of 5, passing through the given points (4, 8) and (-6, 2).
