1 Use the given conditions to write an equation for the line in point-slope form and general form.

To write the equation of a line in point-slope form, you need a point \((x_1, y_1)\) and the slope \(m\). The point-slope form is given by \(y - y_1 = m(x - x_1)\). For the general form, rearrange the point-slope equation into the form \(Ax + By + C = 0\) by moving all terms to one side and ensuring \(A\), \(B\), and \(C\) are integers. For a practical example, if you have a slope of 2 and a point (3, 5), your point-slope equation becomes \(y - 5 = 2(x - 3)\), and when rearranged into general form, it might look like \(2x - y - 1 = 0\). Math can sound daunting, but it’s just puzzles waiting to be solved! Understanding the structure of these equations can be incredibly helpful in fields such as engineering and physics, where slopes represent rates of change (like velocity). Grab a line graph and plot points to visualize how these equations define relationships in real-world scenarios, turning abstract math into tangible concepts!