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In writing an equation of a line, keep in mind that you ALWAYS need the following information in order to establish the linear equation:
1. 2 ordered pairs (x,y) on the line
2. Slope (m)

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.

Select 2 ordered pairs from your table, and substitute those into the slope formula.

Let (x1, y1) = (2, 10)
(x2, y2) = (3, 15)

m = (y2 - y1)/(x2 - x1)
m = (15 — 10)/(3 — 2)
m = 5/1 = 5

Therefore, the slope (m) = 1.

Next, we need to find the value of the y-intercept, (b). 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.

To solve for the y-intercept, we could use one of the given ordered pairs from the table and the slope. We’ll substitute these values into the slope-intercept form:

We’ll use (2, 10) as values for x and y.

y = mx + b
10 = 5(2) + b
10 = 10 + b
Subtract 10 from both sides to solve for b:

10 - 10 = 10 - 10 + b
0 = b

Therefore, the y-intercept is 0.

Now that we have our slope (m = 5), and y-intercept (b = 0), the linear equation is:

y = 5x + 0 or y = 5x

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The vertex of the quadratic function is (1.5, -.75)