How do I find the equation of a line that passes through the point (7, 2) with a slope of 3?

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

y - y1 = m(x - x1)

Where:

  • (x1, y1) is a point on the line (in this case, (7, 2)),
  • m is the slope of the line (in this case, 3).

Now, we can substitute the values we have into this equation:

y - y1 = m(x - x1)

Substituting the values:

y - 2 = 3(x - 7)

Next, we will simplify this equation:

y - 2 = 3x - 21

Now, add 2 to both sides to solve for y:

y = 3x - 21 + 2

Thus:

y = 3x - 19

So, the equation of the line that passes through the point (7, 2) with a slope of 3 is:

y = 3x - 19

This linear equation is now in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. In this case, the slope is 3 and the y-intercept is -19.

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