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Write an equation of the line that passes through the points.

(−4,1),(0,3)

1 Answer

5 votes

Answer:

y = 1/2x + 3

Explanation:

Given at least two points through which a line passes, we can find the equation of a line in slope-intercept form, which is y = mx + b, where

  • m is the slope,
  • and b is the y-intercept

Step 1: We can find the slope using the slope formula, which is

m = (y2 - y1) / (x2 - x1), where (x1, y1) are one point on the line and (x2, y2) is another point on the line.

Allowing (-4, 1) to be our (x1, y1) point and (0, 3) to be our (x2, y2) point, we can find the slope by plugging everything into the formula:

m = (3 - 1) / (0 - (-4))

m = 2 / (0 + 4)

m = 2 / 4

m = 1/2

Step 2: Now we can find b, the y-intercept, by plugging in at least one of the points for x and y and 1/2 for m. Let's use (-4, 1) for x and y:

1 = 1/2(-4) + b

1 = -2 + b

3 = b

Thus, the equation of the line that passes through the points (-4, 1) and (0, 3) is y = 1/2x + 3

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