A line passes through the points (-2,1) and (4,4). Find the equation of the line in the form y = mx + c

In the form y = mx + c, m stands for the slope (or gradient) of the line, and c for its y-intercept. Since we are given two points that are on the line, we can figure out its slope by looking at the vertical and horizontal distance between the two points. Remember that the first coordinate expresses how far right or left a point is, and the second coordinate expresses how far up or down a point is. To get from (-2,1) to (4,4) the line rises a vertical distance of 4 - 1 = 3. So our RISE = 3. The line runs or covers a horizontal distance of 4 - (-2) = 6 between the two points. So our RUN = 6. The slope of the line is simply RISE divided by RUN, or m = 3/6 = 1/2. We now have y = 1/2 x + c. The easiest way to figure out the y-intercept c is to substitute the coordinates of a known point on the line into that equation. Taking for example point (4,4): 4 = 1/2 * 4 + c . We now simply need to rearrange for c: 4 = 2 + c --> c = 2 The solution is then: y = 1/2 x + 2