SOLUTION: Find an equation of the line that satisfies the given conditions. Through (−4, −5); slope :-7/2

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Question 647914: Find an equation of the line that satisfies the given conditions.
Through
(−4, −5);
slope :-7/2

Found 2 solutions by solver91311, MathLover1:
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


Use the point-slope form of an equation of a line:



where are the coordinates of the given point and is the given slope.

John

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Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

a line through
(−4, −5);

slope :

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 (-4, -5)

  • it has a slope of -3.5



First, let's draw a diagram of the coordinate system with point (-4, -5) 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=-3.5, 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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