Write the equation of each line using the given information.
The points (−4,1) and (2,4)both lie on the line.
m=−1 and the point (2,−1) lies on the line.
It has the same slope as y=5 and passes through (1,1).
m=−3 and it has a y-intercept of (0,8)
plz help i don't get any of this.
A. (-4, 1), (2, 4).
m = (y2-y1)/(x2-x1) = (4-1)/(2+4) = 3/6 = 0.5.
Y = mx + b.
1 = 0.5(-4) + b,
b = 3. = y-intercept.
Eq: Y = (1/2)x + 3.
B. (2, -1), m = -1.
Y = mx + b.
-1 = (-1)2 + b,
b = ?
Eq:
C. (1, 1), y = 5.
Y = 5 for all values of x:
(0, 5), (1, 5).
m = (y2-y1)/(x2-x1) = (5-5)/(1-0) = 0/1 = 0.
Y = mx + b.
1 = 0*1 + b,
b = 1.
Eq: Y = 1.
D. m = -3, Yint. = (0, 8).
Y = mx + b.
8 = -3*0 + b,
b = 8.
Eq: Y = -3x + 8.
Sure! I'd be happy to help you with these questions.
For the first question, we are given two points that lie on the line: (-4,1) and (2,4). To find the equation, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m is the slope of the line and b is the y-intercept.
Step 1: Calculate the slope (m)
Using the formula for slope (m):
m = (y2 - y1) / (x2 - x1)
m = (4 - 1) / (2 - (-4))
m = 3 / 6
m = 1/2
Step 2: Find the y-intercept (b)
Using the point-slope form of a linear equation (y - y1 = m(x - x1)):
1 = (1/2)(-4) + b
1 = -2 + b
b = 1 + 2
b = 3
Therefore, the equation of the line is y = (1/2)x + 3.
For the second question, we are given the slope (m = -1) and a point that lies on the line (2, -1). Using the point-slope form, we can plug in the values to find the equation.
Step 1: Plug in the values
Using the point-slope form (y - y1 = m(x - x1)):
y - (-1) = -1(x - 2)
y + 1 = -1(x - 2)
Step 2: Simplify the equation
y + 1 = -x + 2
y = -x + 2 - 1
y = -x + 1
Therefore, the equation of the line is y = -x + 1.
For the third question, we are told that the line has the same slope as y = 5 and passes through the point (1,1). Since the slope is already given, we can directly use it to find the equation.
Step 1: Use the given slope
The slope of y = 5 is 0 since it is a horizontal line. Therefore, the slope of our line is also 0.
Step 2: Plug in the values
Using the point-slope form (y - y1 = m(x - x1)):
y - 1 = 0(x - 1)
y - 1 = 0
y = 1
Therefore, the equation of the line is y = 1.
For the fourth question, we are given the slope (m = -3) and the y-intercept (0,8). The y-intercept is a point at which the line crosses the y-axis, which we can use to find the equation.
Step 1: Plug in the values
Using the slope-intercept form of a linear equation (y = mx + b):
y = -3x + 8
Therefore, the equation of the line is y = -3x + 8.
I hope this helps! Let me know if you have any further questions.