SOLUTION: Find a linear equation whose graph is the straight line with the given properties. Through (23, −5.1) and increasing at a rate of 15 units of y per unit of x.

Question 785318: Find a linear equation whose graph is the straight line with the given properties.
Through
(23, −5.1)
and increasing at a rate of 15 units of y per unit of x.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
If the value of changes by units when the value of changes by ,
then the slope of that line is
and if line goes through (,), then equation will be:

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 (23, -5.1)

it has a slope of 15

First, let's draw a diagram of the coordinate system with point (23, -5.1) 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=15, 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:

since you cannot see a line on a graph above, here is another graph:

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SOLUTION: Find a linear equation whose graph is the straight line with the given properties. Through (23, &#8722;5.1) and increasing at a rate of 15 units of y per unit of x.

SOLUTION: Find a linear equation whose graph is the straight line with the given properties. Through (23, −5.1) and increasing at a rate of 15 units of y per unit of x.