A line passes through (0,2) and (4,10). What is its slope and equation?

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Multiple Choice

A line passes through (0,2) and (4,10). What is its slope and equation?

Explanation:
Finding the slope from two points and then writing the line in slope-intercept form is what's being tested. Compute the slope: m = (10 − 2) / (4 − 0) = 8/4 = 2. With this slope, the line has the form y = 2x + b. Since it passes through (0, 2), plug in: 2 = 2(0) + b, so b = 2. The equation is y = 2x + 2. This also checks the second point: when x = 4, y = 2(4) + 2 = 10. If the slope were 1/2 or -2 or 0, plugging x = 4 would not give y = 10, so those options don’t fit both points.

Finding the slope from two points and then writing the line in slope-intercept form is what's being tested. Compute the slope: m = (10 − 2) / (4 − 0) = 8/4 = 2. With this slope, the line has the form y = 2x + b. Since it passes through (0, 2), plug in: 2 = 2(0) + b, so b = 2. The equation is y = 2x + 2. This also checks the second point: when x = 4, y = 2(4) + 2 = 10. If the slope were 1/2 or -2 or 0, plugging x = 4 would not give y = 10, so those options don’t fit both points.

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