Answer:
Slope-intercept form: is y=3x-10.
Point-slope form: y+4=3(x-2).
Standard form: 3x-y=10.
Step-by-step explanation:
Slope-intercept form is y=mx+b where m is the slope and b is the y-intercept.
A line parallel to y=3x+2 will be of the form y=3x+b where b is not 2.
To find b, we will use that our line goes through (2,-4).
-4=3(2)+b
-4=6+b
Subtract 6 on both sides:
-4-6=b
-10=b
The the line we are looking for in slope-intercept form is y=3x-10.
Standard form is ax+by=c.
y=3x-10
Add 10 on both sides:
10+y=3x
Subtract y on both sides:
10=3x-y
So the equation in standard form is 3x-y=10.
Point-slope form is [tex]y-y_1=m(x-x_1)[/tex].
[tex]y-(-4)=3(x-2)[/tex]
[tex]y+4=3(x-2)[/tex]
Answer:
Step-by-step explanation:
[tex]\text{The slope-intercept form of an equation of a line:}\\\\y=mx+b\\\\m-\text{slope}\\b-\text{y-intercept}\\\\\text{Let}\ k:y=m_1x+b_1,\ l:y=m_2x+b_2\\\\\text{then}\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}[/tex]
[tex]\text{Conclusion:}\\\\\text{Parallel lines have the same slope.}[/tex]
[tex]\text{We have}\ y=3x+2\to m=3[/tex]
[tex]\text{and the point}\ (2,\ -4)\to x=2,\ y=-4.[/tex]
[tex]\text{Substitute to the equation of a line:}\\\\-4=(3)(2)+b\\\\-4=6+b\qquad\text{subtract 6 from both sides}\\\\-10=b\to b=-10[/tex]
[tex]\text{Finally:}\\\\y=3x-10[/tex]
