SOLUTION: Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line

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Question 85069: Write the equation of the line with slope 4 and y-intercept (0, –5). Then graph the line
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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 (0, -5)

  • it has a slope of 4



First, let's draw a diagram of the coordinate system with point (0, -5) plotted with a little blue dot:



Write this down: the formula for the equation, given point x%5B1%5D%2C+y%5B1%5D and intercept a, is

y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 (see a paragraph below explaining why this formula is correct)

Given that a=4, and system%28+x%5B1%5D+=+0%2C+y%5B1%5D+=+-5+%29+, we have the equation of the line:

y=4%2Ax+%2B+-5

Explanation: Why did we use formula y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ? 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 (x%5B1%5D, y%5B1%5D) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (x%5B1%5D, y%5B1%5D): y%5B1%5D+=+a%2Ax%5B1%5D%2Bb Here, we know a, x%5B1%5D, and y%5B1%5D, and do not know b. It is easy to find out: b=y%5B1%5D-a%2Ax%5B1%5D. So, then, the equation of the line is: +y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+.

Here's the graph: