Determine the equations of the following
lines:
(a) having slope ¡1 and passing through (0; 2)
(b) parallel to y=2x-1 and passing through (¡2; 0)
(c) passing through (1; 0) and (¡1; 3)
(d) with x-intercept 6 and y-intercept 3.
I have no clue where to begin.
y-y1=m(x-x1)+b
where m=slope and b=y-intercept
(a)m=1, x1=0, y1=2
(b)since it's parallel, we know that the slopes are equal; m=2
(c)m=(y1-y2)/(x1-x2)
y-y1=m(x-x1)+b
(d)since x-intercept is equal to 6, we know (6, 0). since y-intercept is equal to 3, we know (0,3).
Find the slope: m=(y1-y2)/(x1-x2)
Plug into slope and one of the two coordinates: y-y1=m(x-x1)+b
Thanks so much helps a lot.
Preston, check if the slope shouldn't be
"-1" in
"(a) having slope ¡1 and passing through (0; 2) "
Your computer seems to have a problem getting the negative sign.
yea it is having trouble. thanks again. i am just stuck on my other one now
To determine the equations of the given lines, we can use the point-slope form of a linear equation, which is:
y - y1 = m(x - x1)
Where (x1, y1) represents the coordinates of a point on the line, and m represents the slope of the line.
(a) Slope = -1, and it passes through the point (0, 2):
Using the point-slope form, we have:
y - 2 = -1(x - 0)
y - 2 = -x
y = -x + 2
The equation of the line is y = -x + 2.
(b) Parallel to y = 2x - 1 and passing through (-2, 0):
The given line has a slope of 2. Since the parallel line has the same slope, we can use that in the point-slope form:
y - 0 = 2(x - (-2))
y = 2x + 4
The equation of the line is y = 2x + 4.
(c) Passing through (1, 0) and (-1, 3):
We can calculate the slope using the coordinates of the two points:
slope = (y2 - y1) / (x2 - x1)
slope = (3 - 0) / (-1 - 1)
slope = 3 / -2
slope = -3/2
Using the point-slope form with the slope and one point, let's use (1, 0):
y - 0 = (-3/2)(x - 1)
y = (-3/2)x + (3/2)
The equation of the line is y = (-3/2)x + (3/2).
(d) With x-intercept 6 and y-intercept 3:
To find the equation using the intercepts, we use the slope-intercept form:
y = mx + b, where m is the slope and b is the y-intercept.
Given the x-intercept is 6, we have the point (6, 0). Given the y-intercept is 3, we have the point (0, 3).
To find the slope, we can use the formula:
slope = (y2 - y1) / (x2 - x1) = (0 - 3) / (6 - 0) = -3/6 = -1/2
Using the slope-intercept form, we plug in the slope and the y-intercept:
y = (-1/2)x + 3
The equation of the line is y = (-1/2)x + 3.