Answer: y = 2x - 3.
Explanation:
To write an equation in slope-intercept form, we need to use the given points (2,1) and (0,-3) to find the slope and y-intercept.
The slope, denoted by the letter 'm', represents the rate of change of the line. It can be found using the formula:
m = (y2 - y1) / (x2 - x1)
Let's substitute the coordinates (2,1) and (0,-3) into the formula:
m = (-3 - 1) / (0 - 2)
m = -4 / -2
m = 2
The y-intercept, denoted by the letter 'b', is the y-coordinate where the line intersects the y-axis. To find the y-intercept, we can substitute one of the given points into the slope-intercept form equation:
y = mx + b
Using the point (2,1):
1 = 2(2) + b
1 = 4 + b
b = 1 - 4
b = -3
Now that we have the slope (m = 2) and the y-intercept (b = -3), we can write the equation in slope-intercept form:
y = 2x - 3
Therefore, the equation in slope-intercept form for the given points (2,1) and (0,-3) is y = 2x - 3.
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