When writing an equation of a line, keep in mind that you ALWAYS need two pieces of information when you go to write an equation:
1. ANY point on the line
2. Slope (m)
3. Y-intercept (b)
Once you have these two pieces of information, you plug the x and y values from your point and the slope (m) value into the slope-intercept form, y = mx + b.
Start by solving for the slope of each line. We need two ordered pairs (x, y) from each line to solve for the slope:
Offer A:
(0, 400) and (80, 700)
Let (x1, y1) = (0, 400)
(x2, y2) = (80,700)
m = (y2 - y1)/(x2 - x1)
m = (700 – 400)/(80 – 0) = 300/80 = 15/4
Therefore, the slope (m) for Offer A = 15/4
Next, we need the y-intercept. The y-intercept is the y-coordinate of the point where the graph of the linear equation crosses the y-axis. The y-intercept is also the value of y when x = 0. One of the points we used for solving the slope for Offer A reflects the description for the y-intercept, which is point (0, 400). The y-coordinate is 400–this is the y-intercept of the line.
Now, we can establish the linear equation for Offer A: y = 15/4x + 400
Do the same steps for the other offer:
Offer B:
(0, 500)) and (100,900)
Let (x1, y1) = (0, 500)
(x2, y2) = (100,900)
m = (y2 - y1)/(x2 - x1)
m = (900 - 500)/(100 – 0) = 400/100 = 4
Therefore, the slope for Offer B is 4.
Next, we need the y-intercept. For Offer B, the line crosses at point (0, 500). The y-coordinate, 500 is the y-intercept (b) of the line.
The linear equation for Offer B is:
y = 4x + 500
**NOTE: please double-check the coordinates that I used for solving the slopes of each line before using my inputs. I had a slight difficulty going through the coordinates of your graph because it’s a bit blurry (using my phone to write this post).
Please mark my answers as the Brainliest if you find my explanations helpful :)
