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Find an equation for the line that passes through the points (5,1) and (-4,4) .

User Jfcartier
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Final answer:

To find the equation of the line through (5,1) and (-4,4), calculate the slope, which is -1/3. Then use the point-slope form with one point to create the equation, resulting in y = -1/3x + 8/3.

Step-by-step explanation:

To find an equation for the line that passes through the points (5,1) and (-4,4), we first need to determine the slope of the line.

The slope (m) is calculated by the difference in the y-values divided by the difference in the x-values, which is

(4 - 1) / (-4 - 5). This simplifies to 3 / -9, or -1/3.

With the slope and one of the points, we can use the point-slope form of a line, which is y - y1 = m(x - x1).

Using point (5,1), the equation becomes y - 1 = -1/3(x - 5).

To write this in the slope-intercept form (y = mx + b), we expand and simplify to get y = -1/3x + 5/3 + 1, and

finally, y = -1/3x + 8/3, which is the equation of the line passing through the two given points.

User Jedediah
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