derive the equation of the line in slope-intercept form.
coordinates are (1, 8) and (0, 4) and the line passes through the four on the y-axis.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (1, 8) and (0, 4), we get:
m = (4 - 8) / (0 - 1)
m = (-4) / (-1)
m = 4
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the slope (m = 4) and the coordinates (0, 4), we get:
y - 4 = 4(x - 0)
y - 4 = 4x
To convert this equation to slope-intercept form (y = mx + b), we isolate y:
y = 4x + 4
Since the line passes through the point (0, 4), we substitute the x and y values into the final equation to find the y-intercept (b):
4 = 4(0) + b
4 = 0 + b
b = 4
Therefore, the equation of the line in slope-intercept form is:
y = 4x + 4
write the equation of the line in slope-intercept form.
the coordinates are (0, 2) and (-1, 1) and the line passes through the 2 on the y-axis.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 2) and (-1, 1), we get:
m = (1 - 2) / (-1 - 0)
m = -1 / -1
m = 1
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the slope (m = 1) and the coordinates (0, 2), we get:
y - 2 = 1(x - 0)
y - 2 = x
To convert this equation to slope-intercept form (y = mx + b), we isolate y:
y = x + 2
Since the line passes through the point (0, 2), we substitute the x and y values into the final equation to find the y-intercept (b):
2 = 1(0) + b
2 = 0 + b
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = x + 2
thats wrong..
Apologies for the mistake. Let's correct it.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 2) and (-1, 1), we get:
m = (1 - 2) / (-1 - 0)
m = -1 / -1
m = 1
Now that we have the slope, we can use the slope-intercept form of a linear equation: y = mx + b.
We are given that the line passes through the point (0, 2), which means the y-intercept (b) is 2.
Therefore, the equation of the line in slope-intercept form is:
y = 1x + 2
y = x + 2
that's still wrong. let me say the question again.
write the equation of the line in slope-intercept form.
the coordinates are (0, 2) and (-1, 1) and the line passes through the 2 on the y-axis.
Apologies for the mistake. Let's correct it.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 2) and (-1, 1), we get:
m = (1 - 2) / (-1 - 0)
m = -1 / -1
m = 1
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the slope (m = 1) and the coordinates (0, 2), we get:
y - 2 = 1(x - 0)
y - 2 = x
To convert this equation to slope-intercept form (y = mx + b), we isolate y:
y = x + 2
Since the line passes through the point (0, 2), we substitute the x and y values into the final equation to find the y-intercept (b):
2 = 0 + b
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = x + 2
wait, that was actually *my* mistake, i was wrong. i'm sorry. okay, the coordinates are (0, 2) and (1, -1) and the line passes through the two on the y-axis.
No problem. Let's solve it with the correct information.
To find the equation of the line in slope-intercept form, we first need to find the slope of the line. The slope (m) is given by the formula:
m = (y2 - y1) / (x2 - x1)
Using the coordinates (0, 2) and (1, -1), we get:
m = (-1 - 2) / (1 - 0)
m = -3 / 1
m = -3
Now that we have the slope, we can use the point-slope form of a linear equation:
y - y1 = m(x - x1)
Substituting the slope (m = -3) and the coordinates (0, 2), we get:
y - 2 = -3(x - 0)
y - 2 = -3x
To convert this equation to slope-intercept form (y = mx + b), we isolate y:
y = -3x + 2
Since the line passes through the point (0, 2), we substitute the x and y values into the final equation to find the y-intercept (b):
2 = -3(0) + b
2 = 0 + b
b = 2
Therefore, the equation of the line in slope-intercept form is:
y = -3x + 2