For questions 1-2, find the x- and y- intercepts of the line.
1. -10x+5y=40
D: x-intercept is -4 ; y-intercept is 8
2. 5x+4y=80
D: x-intercept is 16 ; y-intercept is 20
3. Write y=1/6x+4 in standard form using integers
B: -x+6y=24
4.The grocery store sells kumquats for $4.75 a pound and Asian pears for $2.25 a pound. Write an equation in standard form for the weight of kumquats k and Asian pears p that a customer could buy with $22.
A: 4.75k+2.25p=22
5. Graph the equation
x=-2
D: (graph with the vertical line on -2)
These are my answers for Linear Functions: Standard Form (unit 6, lesson 5)
just FYI, the intercept form for a line is
x/a + y/b = 1
if the intercepts are a and b.
So, for #1, just divide by 40 and you have
x/-4 + y/8 =1
x - intercept is point where y = 0
y - intercept is point where x = 0
1. Correct answer.
2.
5 x + 4 y = 80
x - intercept
5 x + 4 • 0 = 80
5 x = 80
x = 80 / 5 = 16
y - intercept
5 • 0 + 4 y = 80
4 y = 80
y = 80 / 4 = 20
3.
The standard form of a line is in the form:
Ax + By = C
where
A is a positive integer
B and C are integers
y = 1 / 6 x + 4
Multiply both sides by 6
6 y = x + 24
Subtract 6y to bith sides.
0 = x + 24 - 6 y
Subtract 24 y to bith sides.
- 24 = x - 6 y
x - 6 y = - 24
4. Correct answer.
5. Correct answer.
To find the x- and y-intercepts of a line, we need to understand what these terms mean.
The x-intercept is the point where the line crosses the x-axis. To find it, we set y equal to zero in the equation and solve for x.
The y-intercept is the point where the line crosses the y-axis. To find it, we set x equal to zero in the equation and solve for y.
Now let's solve the given equations to find the x- and y-intercepts:
1. -10x + 5y = 40
To find the x-intercept, we set y = 0:
-10x + 5(0) = 40
-10x = 40
x = -4
So the x-intercept is (-4, 0).
To find the y-intercept, we set x = 0:
-10(0) + 5y = 40
5y = 40
y = 8
So the y-intercept is (0, 8).
2. 5x + 4y = 80
To find the x-intercept, we set y = 0:
5x + 4(0) = 80
5x = 80
x = 16
So the x-intercept is (16, 0).
To find the y-intercept, we set x = 0:
5(0) + 4y = 80
4y = 80
y = 20
So the y-intercept is (0, 20).
3. To write y = (1/6)x + 4 in standard form using integers, we need to eliminate the fraction. We can do this by multiplying every term by 6:
6y = x + 24
Then we rearrange the equation to have x and y on the same side:
-x + 6y = 24
So the standard form is -x + 6y = 24.
4. The equation for the weight of kumquats k and Asian pears p that a customer could buy with $22 is expressed as:
4.75k + 2.25p = 22
5. The equation x = -2 represents a vertical line passing through the x-coordinate -2. To graph this, you simply draw a vertical line on the coordinate plane at x = -2.