What is the equation of the line with slope 2 through (1, 14)?

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Multiple Choice

What is the equation of the line with slope 2 through (1, 14)?

Explanation:
When a line’s slope and a point on the line are known, use the point-slope form: y − y1 = m(x − x1). With m = 2 and the point (1, 14), this becomes y − 14 = 2(x − 1). Simplifying gives y − 14 = 2x − 2, so y = 2x + 12. This also matches the intercept b = y1 − m x1 = 14 − 2(1) = 12. Substituting x = 1 yields y = 14, confirming the point lies on the line. Lines with the opposite slope or a different intercept wouldn’t pass through (1, 14). The equation is y = 2x + 12.

When a line’s slope and a point on the line are known, use the point-slope form: y − y1 = m(x − x1). With m = 2 and the point (1, 14), this becomes y − 14 = 2(x − 1). Simplifying gives y − 14 = 2x − 2, so y = 2x + 12. This also matches the intercept b = y1 − m x1 = 14 − 2(1) = 12. Substituting x = 1 yields y = 14, confirming the point lies on the line. Lines with the opposite slope or a different intercept wouldn’t pass through (1, 14). The equation is y = 2x + 12.

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