Question
(1,3),(0,-2) use the graph to derive the equation of the line in slope-intercept form.
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GPT 3.5
To find the equation of the line in slope-intercept form, we first need to determine the slope of the line. The slope, denoted by m, can be determined using the formula:
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Let's use the points (1,3) and (0,-2) to find the slope:
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5
Now that we know the slope is 5, we can use the slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
To find the y-intercept, we can use any point on the line. Let's use (1,3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 2
m = (y2 - y1) / (x2 - x1)
where (x1, y1) and (x2, y2) are two points on the line.
Let's use the points (1,3) and (0,-2) to find the slope:
m = (3 - (-2)) / (1 - 0)
m = 5 / 1
m = 5
Now that we know the slope is 5, we can use the slope-intercept form of a line:
y = mx + b
where m is the slope and b is the y-intercept.
To find the y-intercept, we can use any point on the line. Let's use (1,3):
3 = 5(1) + b
3 = 5 + b
b = 3 - 5
b = -2
Therefore, the equation of the line in slope-intercept form is:
y = 5x - 2
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