Find the slope and y- intercept of a line by writing the equation in slope- intercept form.Hint: Convert the given equation form into the slope-intercept form as deemed necessary:
a. y=4-2/3 x
b. 3x+7y-10=0
c. y-4=2x
d. 2y-10=2x
If a, b, c and d are not answers but questions then:
Slope-intercept form of a straight line is:
y = m x + b
m is the slope
b is the y intercept
a.
y = 4 - 2 / 3 x
y = - 2 / 3 x + 4
slope = - 2 / 3 , y - intercept = 4
b.
3 x + 7 y - 10 = 0
Subtract 3 x to both sides
7 y - 10 = - 3 x
Add 10 to both sides
7 y = - 3 x + 10
Divide both sides by 7
y = - 3 / 7 x + 10 / 7
slope = - 3 / 7 , y - intercept = 10 / 7
c.
y - 4 = 2 x
Add 4 to both sides
y = 2 x + 4
slope = 2 , y - intercept = 4
d.
2 y - 10 = 2 x
Add 10 to both sides
2 y = 2 x + 10
Divide both sides by 2
y = x + 5
slope = 1 , y - intercept = 5
a. To convert the equation y = 4 - (2/3)x into slope-intercept form, we rearrange it to isolate y:
y = -(2/3)x + 4
So, the slope is -(2/3) and the y-intercept is 4.
b. To convert the equation 3x + 7y - 10 = 0 into slope-intercept form, we solve for y:
7y = -3x + 10
y = (-3/7)x + 10/7
Here, the slope is (-3/7) and the y-intercept is 10/7.
c. To convert the equation y - 4 = 2x into slope-intercept form, we isolate y:
y = 2x + 4
The slope is 2 and the y-intercept is 4.
d. To convert the equation 2y - 10 = 2x into slope-intercept form, we solve for y:
2y = 2x + 10
y = x + 5
In this case, the slope is 1 and the y-intercept is 5.
Remember, there's no need to be Slope's nope, these answers are straight up!
To find the slope and y-intercept of a line, we need to write the equation of the line in slope-intercept form, which has the general form: y = mx + b.
a. y = 4 - (2/3)x:
To convert the given equation into slope-intercept form, we simply need to rearrange the equation to solve for y.
1. Start with: y = 4 - (2/3)x.
2. Rearrange the equation to isolate y by moving the terms to the appropriate sides of the equation.
Subtract 4 from both sides:
y - 4 = - (2/3)x.
3. Now we have the equation in slope-intercept form. The coefficient of x (-2/3) represents the slope and the constant term (-4) represents the y-intercept.
Therefore, the slope is -2/3 and the y-intercept is -4.
b. 3x + 7y - 10 = 0:
1. Start with: 3x + 7y - 10 = 0.
2. Rearrange the equation to solve for y.
Move the 3x term to the other side by subtracting 3x from both sides:
7y = -3x + 10.
3. Divide through by 7 to isolate the y variable:
y = (-3/7)x + (10/7).
4. Now we have the equation in slope-intercept form. The coefficient of x (-3/7) represents the slope, and the constant term (10/7) represents the y-intercept.
Therefore, the slope is -3/7 and the y-intercept is 10/7.
c. y - 4 = 2x:
1. Start with: y - 4 = 2x.
2. Rearrange the equation to solve for y.
Add 4 to both sides:
y = 2x + 4.
3. Now we have the equation in slope-intercept form. The coefficient of x (2) represents the slope, and the constant term (4) represents the y-intercept.
Therefore, the slope is 2, and the y-intercept is 4.
d. 2y - 10 = 2x:
1. Start with: 2y - 10 = 2x.
2. Rearrange the equation to solve for y.
Add 10 to both sides:
2y = 2x + 10.
3. Divide through by 2 to isolate the y variable:
y = x + 5.
4. Now we have the equation in slope-intercept form. The coefficient of x (1) represents the slope, and the constant term (5) represents the y-intercept.
Therefore, the slope is 1, and the y-intercept is 5.