Final answer:
The equation of the line passing through the points (3, 10) and (-1, 2) is y = 2x + 4, obtained by first calculating the slope (m = 2) and then applying it to the point-slope form of the linear equation.
Step-by-step explanation:
To find the equation of the line passing through the points (3, 10) and (-1, 2), you need to calculate the slope (m) and use the point-slope form or the y-intercept form of a linear equation.First, calculate the slope using the formula m = (y2 - y1) / (x2 - x1). Plugging in the values from the points, you get m = (2 - 10) / (-1 - 3) = (-8) / (-4) = 2. The slope of the line is 2.
Now, you can use the point-slope form of the equation: y - y1 = m(x - x1), which can also be converted into the slope-intercept form, y = mx + b. Using one of the given points, such as (3, 10), you can write the equation as y - 10 = 2(x - 3). Simplifying, y - 10 = 2x - 6, and then y = 2x + 4.The equation of the line is y = 2x + 4.To find the equation of the line between the points (3, 10) and (-1, 2), we need to first find the slope of the line using the formula:slope = (y2 - y1) / (x2 - x1)Using the points (3, 10) and (-1, 2), we have:slope = (2 - 10) / (-1 - 3) = -8 / -4 = 2Next, we can use the point-slope form of a linear equation to find the equation of the line:y - y1 = m(x - x1)Using the point (3, 10) and slope of 2, we have:y - 10 = 2(x - 3)y - 10 = 2x - 6y = 2x + 4Therefore, the equation of the line between the points (3, 10) and (-1, 2) is y = 2x + 4.