1. Find the slope of the line passing through the points (-1, 2), (0, 5).
2. Suppose y varies directly with x, and y = 15 and x = 5.
Write a direct variation equation that relates x and y.
What is the value of y when x = 9?
3. Write an equation in slope-intercept form of the line
which went through (-3, 4) and (1. 4).
4. Use the point-slope form to write the equation of a line
which has a slope of 2/3
and goes through (-3, -1).
Write your final equation in slope-intercept form.
5. Write the equation in standard form using whole numbers
(no fractions or decimals): = −2/3 − 1
I do NOT ask for answers. I’m just asking someone to explain the concepts of these because I don’t understand at all #1 the slope of a line is the change in y divided by the change in x. You can select any two points on the line. Then just apply the formula you have:
slope = (y2-y1)/(x2-x1)
which divides the change in y by the change in x
#2 y varies directly with x, means that
y=kx
for some value of k. Or, you can see it means that
y/x = k
is a constant for two values of x and y involved. So you want it like
a/9 = 15/5
You don’t even need to know what k is, although it is clear that k=3 in this problem.
#3 y = mx+b
So just plug in your two points to get two equations to solve for m and b. However, see #4 if you want to see another way. (it uses #1 to find the slope)
#4 Since the slope of a line is constant, it is the same between any two points on the line. In particular, if one of the points is (-3,-1) and the other is any (x,y) we have (from #1)
[y-(-1)]/[x-(-3)] = 2/3
Or, as it is more often written,
y+1 = 2/3 (x+3)
You should now see how all of these problems use the idea of slopes and points on lines.
#5 I can’t say; something is missing. But whatever form you come up with, just rearrange the terms into a standard form by erasing the fractions. For instance,
y = -2/3 x – 1 can be rearranged via
3a = -2x-3
2x + 3y = -3 OHHHHHHHH ok that’s so much more since, THANKS A LOT Steve are from Connexus ALEGRBA 1A UNIT 6 LESSON 6 Parallel and perpendicular lines, use this.
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GOOD LUCK!
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