Write an equation of a line that passes through the points (4, -1) and (-2, 3) in slope-intercept form (y= mx + b).
Question
Write an equation of a line that passes through the points (4, -1) and (-2, 3) in slope-intercept form (y= mx + b).
Solution
Sure, here are the steps to find the equation of a line that passes through the points (4, -1) and (-2, 3) in slope-intercept form (y= mx + b).
Step 1: Find the slope (m) of the line. The formula to find the slope when given two points, (x1, y1) and (x2, y2), is (y2 - y1) / (x2 - x1).
So, m = (3 - (-1)) / (-2 - 4) = 4 / -6 = -2/3.
Step 2: Use the slope-intercept form, y = mx + b, and one of the points to solve for b. Let's use the point (4, -1).
-1 = -2/3 * 4 + b -1 = -8/3 + b -1 + 8/3 = b b = -3/3 + 8/3 = 5/3
Step 3: Write the equation of the line using the slope and y-intercept.
So, the equation of the line is y = -2/3x + 5/3.
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