Question

1. Find the slope of the line that passes 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
that passed through (-3, 4) and (1. 4).

4. Use point-slope form to write the equation of a line
that has a slope of 2/3
and passes through (-3, -1).
Write your final equation in slope-intercept form.

5. Write the equation in standard form using integers
(no fractions or decimals): = −2/3 − 1


I'm NOT asking for answers. I'm simply asking for someone to explain the concepts of these because I don't understand at all

Answer 1

#1 the slope of a line is the change in y, divided by the change in x. You can pick any two points on the line. Then just apply the formula you have:

slope = (y2-y1)/(x2-x1)

which divides y-change by x-change

#2 y varies directly with x, means that
y = kx
for some value of k. Or, you can see that this means that

y/x = k

is a constant for any two values of x and y involved. So, you want y such that

y/9 = 15/5

You don't even need to know what k is, though clearly 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 usually written,
y+1 = 2/3 (x+3)

By now you should see how all these problems use the idea of slopes and points on lines.

#5 I can't tell; something's missing. But whatever form you come up with, just rearrange the terms to standard form by clearing fractions. For example,

y = -2/3 x - 1 can be rearranged via
3y = -2x-3
2x + 3y = -3

Answer 2

OHHHHHHHH ok that makes so much more since, THANK YOU SO MUCH Steve

Answer 3

If u guys are from Connexus ALEGRBA 1A UNIT 6 LESSON 6 Parallel and Perpendicular Lines practice is use this.
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GOOD LUCK!
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Answer 4

Find the slope of a line that passes through the point (3,5) and (–6,–10)

Answer 5

this is U6L9 not U6L6