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 (-6,20) and (3, -1)."

Answer 1

To find the equation of a line using the slope-intercept form, we can use the given points (-6,20) and (3, -1). First calculate the slope using the formula (y2 - y1) / (x2 - x1), then substitute the coordinates of one of the points into the equation to find the y-intercept.

Step-by-step explanation:

To find the equation of a line using the slope-intercept form (y = mx + b), we need to know the slope and a point on the line. Let's use the given points (-6,20) and (3, -1) to find the equation of the line:

First, find the slope (m) using the formula (y2 - y1) / (x2 - x1). In this case, the slope is (-1 - 20) / (3 - (-6)) = -21 / 9 = -7/3.

Next, choose one of the points (let's use (-6,20)) and substitute its coordinates into the slope-intercept form equation (y = mx + b) to find the value of b. We have 20 = (-7/3)(-6) + b.

Simplifying this equation, we get b = 20 - 14 = 6.

Now that we have the slope (m = -7/3) and the y-intercept (b = 6), we can write the equation of the line: y = (-7/3)x + 6.