A line has a slope of 6/7 and a y-intercept of -5. Which of the following is the equation of the line?
7x - 6y = -35
7x - 6y = -5
6x - 7y = 35
6x - 7y = -35
I'm honestly not sure with this, I'm thinking that it's 7x - 6y = -5.. Not sure though.
Also, could you explain how you found your answer? This would help so much..
y = m x + b
This is called the slope-intercept form because "m" is the slope and "b" gives the y-intercept.
In this case :
b = 6 / 7
m = - 5
y = m x + b
y = ( 6 / 7 ) x + ( - 5 )
y = ( 6 / 7 ) x - 5 Multiply both sides by 7
7 y = 6 x - 35 Subtract 6 x to both sides
7 y - 6 x = 6 x - 35 - 6x
7 y - 6 x = - 35 Multiply both sides by - 1
- 7 y + 6 x = 35
6 x - 7 y = 35
Correction:
In this case :
m = 6 / 7
b = - 5
To find the equation of a line when given its slope and y-intercept, you can use the slope-intercept form of a linear equation, which is y = mx + b.
In this case, the slope is 6/7 and the y-intercept is -5. So the equation will have the form y = (6/7)x - 5.
Now let's analyze the answer choices:
1. 7x - 6y = -35
2. 7x - 6y = -5
3. 6x - 7y = 35
4. 6x - 7y = -35
We want to rewrite each equation in the form y = mx + b.
1. Divide both sides of the equation by -6 to isolate y:
-(7/6)x + 35/6 = y
Thus, the equation is y = -(7/6)x + 35/6, which is not equivalent to the slope-intercept form.
2. Divide both sides of the equation by -6 to isolate y:
-(7/6)x + 5/6 = y
Thus, the equation is y = -(7/6)x + 5/6, which is not equivalent to the slope-intercept form.
3. Divide both sides of the equation by -7 to isolate y:
-(6/7)x - 35/7 = y
Simplifying, the equation is y = -(6/7)x - 5, which is in the slope-intercept form.
4. Divide both sides of the equation by -7 to isolate y:
-(6/7)x - 35/7 = y
Simplifying, the equation is y = -(6/7)x - 5, which is also in the slope-intercept form.
Thus, the correct equation of the line is y = -(6/7)x - 5. So the answer is either choice 3 or 4.