The line with slope -3 passing through (2,7) has which slope-intercept form?

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Multiple Choice

The line with slope -3 passing through (2,7) has which slope-intercept form?

Explanation:
In slope-intercept form, a line is written as y = mx + b, where m is the slope and b is the y-intercept. The slope here is -3, so the equation starts as y = -3x + b. Use the given point (2, 7) to find b: 7 = -3(2) + b, which gives 7 = -6 + b, so b = 13. Therefore, the line is y = -3x + 13. Quick check: plugging in x = 2 yields y = -3(2) + 13 = -6 + 13 = 7, which matches the point. Other forms would not produce y = 7 when x = 2, so they don’t pass through the given point.

In slope-intercept form, a line is written as y = mx + b, where m is the slope and b is the y-intercept. The slope here is -3, so the equation starts as y = -3x + b. Use the given point (2, 7) to find b: 7 = -3(2) + b, which gives 7 = -6 + b, so b = 13. Therefore, the line is y = -3x + 13. Quick check: plugging in x = 2 yields y = -3(2) + 13 = -6 + 13 = 7, which matches the point. Other forms would not produce y = 7 when x = 2, so they don’t pass through the given point.

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