Short Answer 
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. By calculating the slope from points (0, 5) and (-6, 14), the slope is found to be -1.5, leading to the equation y = -1.5x + 5, which can be graphically represented by plotting the points and drawing the line through them.
Step 1: Understand Slope-Intercept Form
The equation of a line in slope-intercept form is expressed as y = mx + b, where m represents the slope and b represents the y-intercept. In this case, the line is given as y = kx + 5. Here k replaces the slope, and 5 is the y-intercept. Your goal is to find the value of k to complete the equation of the line.
Step 2: Calculate the Slope
The slope is calculated using the formula (y2 – y1) / (x2 – x1), which requires two points. You have one given point (0, 5), which corresponds to the y-intercept. For the second point, use (-6, 14). Plugging in these coordinates, the slope calculation looks as follows:
- y1 = 5, y2 = 14
- x1 = 0, x2 = -6
- Plug into the slope formula: (14-5) / (-6-0) = 9 / -6 = -3/2
This results in a slope of -1.5, indicating that for every 2 units you move horizontally, the line drops 3 units vertically.
Step 3: Graph the Line
With the slope calculated, you can substitute it back into the slope-intercept form of the equation, resulting in y = -1.5x + 5. To graph this line, start by plotting the two points (-6, 14) and (0, 5). After plotting these points, draw a straight line through them. You can find additional points by moving along the slope: from any point, move 3 units up and 2 units left or vice versa to locate additional points on the line.