What is the y-intercept of y =
2/3x + 2?
I have to write it out but how?
A line has a slope of
1/2 and passes through the point (0,5). What is the equation of the line?
A)y = 1/2x + 5
B)y = 1/2x - 5<---
C)y = 5x + 1/2
D)y = -5x + 1/2
Find an equation of the line that passes through the points (1,2) and (2,3).
A) y = x - 1
B) y = x + 1
C) y = x - 2 <--
D) y = 2x - 1
8)Find an equation of the line that has intercepts (1,0) and (0,4).
A) y = 4x - 1 <--
B) y = -4x + 4
C) y = -4x + 1
D) y = -4x - 4
9)A line passes through the point (2, 3) and has a slope of -2. Which is the equation of the line in point-slope form?
A) 2x + y = 7
B) y = -2x + 7
C) y - 3 = -2(x - 2)<---
D) y = -1/2x + 5
1. is -2?
The probability of guessing them all wrong would be (3/4)^5 = .24
You managed to get the all wrong
1. In the form y = mx + b
the y-intercept is b
in the equation y = (2/3)x + 2, what do you see in place of the b ?
2. isn't (0,5) the y-intercept ?
so b = 5
which equation has 1/2 in front of the x and a 5 instead of the b ?
3. I subbed (1,2) into your choice and it did not work, no point trying the 2nd point.
Look at the points, in each case the y is 1 more than the x
Look at y = x+1
To me that says, the y is 1 more than the x
4.
Again isn't (0,4) the y-intercept?
So which equation has +4 at the end ?
5.
Only B and D are in slope - yintercept form, ruling out A and C
Which of B and D has a slope of -2 ?
Sub in (2,3) in your choice to make sure
1. +2
2. y = 1/2x + 5 .. I had -5
3. y = x + 1
4. y = -4x + 4.
5. y = -2x + 7
thanks !
To find the y-intercept of an equation in the form y = mx + b, where m is the slope and b is the y-intercept, you need to identify the value of b.
In the equation y = (2/3)x + 2, the y-intercept is the value of y when x is 0. To find it, substitute x = 0 in the equation:
y = (2/3)(0) + 2
y = 0 + 2
y = 2
So, the y-intercept of the equation y = (2/3)x + 2 is 2.
For the second question, to find the equation of a line with a given slope and passing through a given point, you can use the point-slope form of a linear equation, which is:
y - y₁ = m(x - x₁)
where (x₁, y₁) is the given point and m is the slope.
Using the point (0, 5) and the slope 1/2, substitute these values into the point-slope form:
y - 5 = (1/2)(x - 0)
y - 5 = (1/2)x
y = (1/2)x + 5
So, the equation of the line is y = (1/2)x + 5. Hence, the answer is option A.
For the third question, to find the equation of a line passing through two given points (x₁, y₁) and (x₂, y₂), you can use the slope-intercept form of a linear equation, which is:
y = mx + b
where m is the slope and b is the y-intercept.
Using the points (1,2) and (2,3), you can calculate the slope:
m = (y₂ - y₁) / (x₂ - x₁)
m = (3 - 2) / (2 - 1)
m = 1
Now that you have the slope, substitute one of the given points and the slope into the slope-intercept form:
2 = 1(1) + b
2 = 1 + b
b = 2 - 1
b = 1
So, the equation of the line passing through the points (1,2) and (2,3) is y = x - 1. Hence, the answer is option A.
For the fourth question, to find the equation of a line with x-intercept (a, 0) and y-intercept (0, b), you can use the slope-intercept form.
Using the intercepts (1,0) and (0,4), you can calculate the slope:
m = (0 - 4) / (1 - 0)
m = -4 / 1
m = -4
Now that you have the slope, substitute the slope and one of the intercepts into the slope-intercept form:
0 = -4(1) + b
0 = -4 + b
b = 0 + 4
b = 4
So, the equation of the line with intercepts (1,0) and (0,4) is y = -4x + 4. Hence, the answer is option A.
For the fifth question, to find the equation of a line passing through a given point (x₁, y₁) with a given slope m, you can use the point-slope form.
Using the point (2,3) and slope -2, substitute these values into the point-slope form:
y - 3 = -2(x - 2)
Distribute and simplify:
y - 3 = -2x + 4
y = -2x + 7
So, the equation of the line passing through the point (2,3) with a slope of -2 is y = -2x + 7. Hence, the answer is option B.