Answer:
y = 3x -4
Explanation:
The two pairs of x and y values are used to find the slope of the line. That and one of the pairs is used to find the y-intercept. These values are put into the slope-intercept equation to give the equation of the line through the two points.
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Each (x, y) pair represents a point on a graph. The slope-intercept equation for a line relates all the (x, y) pairs that lie on the line. That equation is ...
y = mx +b . . . . . . where m is the slope, and b is the y-intercept
slope
The slope is the "steepness" of the line. It is positive when the line goes up to the right, and negative when the line goes down to the right. It is 0 for a horizontal line.
The slope is found from (x, y) pairs using the formula ...
m = (y2 -y1)/(x2 -x1) . . . . . . where (x1, y1) and (x2, y2) refer to different pairs
m = (8 -(-1))/(4 -1) = 9/3 = 3 . . . . using the (x, y) values from the table
y-intercept
The y-intercept (b) is the y-value where the line crosses the y-axis. It can be found by rearranging the slope-intercept equation shown above:
b = y - mx . . . . . . . for a line with slope m and a point (x, y) on the line
Using the first point listed in the table with the value of m we just found, we see that b is ...
b = -1 - 3(1) = -4 . . . . . . for (x, y) = (1, -1) and m = 3
equation
Now that we have found m=3 and b=-4 for the points in the table, we can put these values in the slope-intercept equation:
y = mx +b
y = 3x -4 . . . . . equation of the relationship in the table