through: (2,5), slope = 3

Answer 1

To find the equation of a line given a point and the slope, you can use the point-slope form of a linear equation, which is:

\[ y - y_1 = m(x - x_1) \]

where \((x_1, y_1)\) is the point on the line, and \(m\) is the slope.

In your case, the point is \((2, 5)\) and the slope \(m\) is 3. Plugging these values into the formula:

\[ y - 5 = 3(x - 2) \]

Now, simplify the equation:

1. Distribute the slope on the right side: \[ y - 5 = 3x - 6 \]

2. Add 5 to both sides: \[ y = 3x - 6 + 5 \]

3. Combine the constants: \[ y = 3x - 1 \]

So, the equation of the line that passes through the point (2, 5) with a slope of 3 is:

\[ y = 3x - 1 \]