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Question 904940: Write the equation of a line with a slope of and a y-intercept of (0, -2).
Write the equation of a line with a slope of -4 passing through the point (-3,-1).
Write the equation of the line that passes through the points (2,-6) and (-2,-4).
Write the equation of a line parallel to the line 2x - 5y = 10 with a y-intercept of (0,-1). Write your answer in standard form.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! 1.
Using the slope-intercept form,
 where  and 
where m=slope, b=y-intercept,
and, substituting the values  and  ,
And the general equation is, 
2.
Write the equation of a line with a slope of  passing through the point (-3,-1).
| Solved by pluggable solver: FIND a line by slope and one point |
What we know about the line whose equation we are trying to find out:
- it goes through point (-3, -1)
- it has a slope of -4
First, let's draw a diagram of the coordinate system with point (-3, -1) plotted with a little blue dot:
Write this down: the formula for the equation, given point  and intercept a, is
 (see a paragraph below explaining why this formula is correct)
Given that a=-4, and  , we have the equation of the line:
Explanation: Why did we use formula  ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point ( ,  ) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (, ):  Here, we know a, , and , and do not know b. It is easy to find out:  . So, then, the equation of the line is:  .
Here's the graph:
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3.
Write the equation of the line that passes through the points (2,-6) and (-2,-4).
| Solved by pluggable solver: FIND EQUATION of straight line given 2 points |
hahaWe are trying to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (2, -6) and (x2, y2) = (-2, -4).
Slope a is  .
Intercept is found from equation  , or  . From that,
intercept b is , or  .
y=(-0.5)x + (-5)
Your graph:
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4.
Write the equation of a line parallel to the line  with a y-intercept of (0,-1).
...solve for  first
| Solved by pluggable solver: Finding the Equation of a Line Parallel or Perpendicular to a Given Line |
Since any two parallel lines have the same slope we know the slope of the unknown line is  (its from the slope of  which is also ).
Also since the unknown line goes through (0,-1), we can find the equation by plugging in this info into the point-slope formula
Point-Slope Formula:
 where m is the slope and (,) is the given point
 Plug in  ,  , and 
 Distribute
 Multiply
 Subtract  from both sides to isolate y
 Combine like terms
So the equation of the line that is parallel to and goes through ( ,) is
So here are the graphs of the equations and
 graph of the given equation (red) and graph of the line (green) that is parallel to the given graph and goes through (,)
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