Question

If the slope of a line and a point on the line are known, the equation of the line can be found using the slope-intercept form, y=mx+b. To do so, substitute the value of the slope and the values of x and y using the coordinates of the given point, then determine the value of b.

Using the above technique, find the equation of the line containing the points (8,13) and (4,2).

Answer 1

To find the equation of a line, calculate the slope from two points, then use one point to solve for the y-intercept in the slope-intercept form. The equation of the line through (8,13) and (4,2) is y = (11/4)x - 3.

Step-by-step explanation:

To find the equation of a line with a known slope and a specific point, you can use the slope-intercept form of a line, which is y = mx + b. Here, 'm' represents the slope, and 'b' represents the y-intercept. First, calculate the slope using the formula which is the change in y (rise) divided by the change in x (run). With the points (8,13) and (4,2), the slope (m) is (13 - 2) / (8 - 4) = 11 / 4. Now you have the slope of the line.

Once you have the slope, substitute the slope and the coordinates of one point into the equation to solve for b. Using the point (8,13), the equation becomes 13 = (11/4)(8) + b. Solve for b, yielding b = -3. Now the equation of the line can be written as y = (11/4)x - 3.

This is a systematic method to find the linear equation given two points. Applying this process allows us to clearly understand how each component of the equation represents different aspects of the line's graph on a coordinate plane.