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Question 113203: I need help on the following questions:I am having a hard time with finding slopes and writing the following equations. I would really appreciate your help,thank you in advance.
1.Find the slope of the line passing through the points (-3,1) and (-6,10)
2. Write the equation of the line with slope -5 and y intercept (0,5)
3. Write the equation of the line with x-intercept (-1,0) and undefined slope
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! To find the slope of a line given two points, the first thing to decide is which will be Point 1 and which Point 2. It doesn't matter which you pick, as long as you keep it consistent as you solve the problem.
Let's say that your point (-3, 1) is  and (-6, 10) is 
The coordinates of are  and  , and
The coordinates of are  and 
Now we can use the formula for the slope to compute it.
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The slope-intercept form of a straight line is  where m is the slope and b is the y-coordinate of the y-intercept. The y-intercept is the point where the line intersects the y-axis, in other words, the value of y when x = 0.
Given that the slope of the line is -5 and the y-intercept is (0, 5), we can write the equation directly by substitution in the slope-intercept form.
Can you see that if you put 0 in for x in this equation that y = 5?
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A line with an undefined slope is a line where all of the x-coordinate points are equal. That means that if you tried to compute the slope, the slope formula,  would have a zero denominator. Such a line must be a vertical line for all of the x-coordinates to be equal.
Since all of the x-coordinates are equal, we know what that value is from the x-coordinate of the x-intercept, (-1, 0). Since x = -1 for all values of y, the equation  fully describes the line and is therefore the sought after equation.
Hope this helps,
John
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