Question
slope form for (-4,1),(2,3)
Answers
GPT 3.5
The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.
To find the slope (m) of the line passing through the points (-4, 1) and (2, 3), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we have:
m = (3 - 1) / (2 - (-4))
= 2 / 6
= 1/3
Now we have the value of the slope (m = 1/3). To find the equation in slope-intercept form, we need to determine the y-intercept (b).
Using the point-slope form of the linear equation (y - y1) = m(x - x1), let's take the point (-4, 1):
(y - 1) = (1/3)(x - (-4))
y - 1 = (1/3)(x + 4)
y - 1 = (1/3)x + 4/3
To convert this equation to slope-intercept form, we isolate y:
y = (1/3)x + 4/3 + 1
= (1/3)x + 4/3 + 3/3
= (1/3)x + 7/3
Therefore, the slope form for the line passing through the points (-4, 1) and (2, 3) is y = (1/3)x + 7/3.
To find the slope (m) of the line passing through the points (-4, 1) and (2, 3), we can use the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the coordinates, we have:
m = (3 - 1) / (2 - (-4))
= 2 / 6
= 1/3
Now we have the value of the slope (m = 1/3). To find the equation in slope-intercept form, we need to determine the y-intercept (b).
Using the point-slope form of the linear equation (y - y1) = m(x - x1), let's take the point (-4, 1):
(y - 1) = (1/3)(x - (-4))
y - 1 = (1/3)(x + 4)
y - 1 = (1/3)x + 4/3
To convert this equation to slope-intercept form, we isolate y:
y = (1/3)x + 4/3 + 1
= (1/3)x + 4/3 + 3/3
= (1/3)x + 7/3
Therefore, the slope form for the line passing through the points (-4, 1) and (2, 3) is y = (1/3)x + 7/3.