To find the equation of the line in slope-intercept form, y = mx + b, we can start by solving for the slope. The slope compares the vertical change (the rise) to the horizontal change (the run) when moving from one fixed point to another along the line.
The slope formula is:
m = (y2 - y1)/(x2 - x1)
We need to select 2 pairs of points from your given table.
Let (x1, y1) = (1, 8)
(x2, y2) = (2, 10)
Plug these values into the formula:
m = (y2 - y1)/(x2 - x1)
m = (10 — 8)/(2 — 1)
m = 2/1 or 2.
Therefore, the slope of the line is 2.
Next, we need to figure out what the y-intercept of the line is. The y-intercept is the point where the line crosses the y-axis. The y-intercept is also the value of y when x = 0.
Looking at your given table, you have an ordered pair, (0, 6) — this is the y-intercept. The y-coordinate (6) is the value of “b” in the slope-intercept form, y = mx + b.
Now that we have our slope (m) = 2, and y-intercept (b) = 6, we can write our equation as follows:
y = 2x + 6
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