ACT Preparation / Unit 9 ACT 0813 worked example, 60 to 90 seconds
The Line Through Two Points
The idea
To write the equation of the line through two points, work in three steps. First, find the slope from the two points. Second, put the slope and either point into point-slope form. Third, rearrange to the form the question asks for, and check that the other point satisfies the equation.
In practice
Worked example: through (−1, 4) and (3, −4). Step one: m = (−4 − 4)/(3 − (−1)) = −8/4 = −2. Step two: y − 4 = −2(x + 1). Step three: y = −2x + 2. Check the other point: −2(3) + 2 = −4, so it fits.
Where people slip
Either point gives the same final equation. If the two points lead to different equations, look for a sign error in the slope, often from subtracting in different orders.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
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