Will the value of this slope be positive or negative?
2 answers:
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You only flip the inequality sign when you multiply or divide both sides by a negative number.
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Problem 1
The inequality sign flip happens because we divided both sides by -8.
The graph will have a closed circle at 4 with shading to the left.
Three solutions are x = 0, x = 1, x = 2. You can pick any three numbers you want as long as they are 4 or smaller.
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Problem 2
The graph will have an open circle at 13/3 = 4&1/3 = 4.333 approx. The shading is to the left. No inequality sign flip happens because we divided both sides by a positive number.
Your choice of three solutions is correct. You can pick anything smaller than 4.3333
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Problem 3
The solution set is any value 3 or larger. Three solutions are x = 5, x = 6 and x = 7.
The graph has a closed circle at 3 on the number line. The shading is to the right.
Answer:
Step-by-step explanation:
1) First, find the slope of the line. Use the slope formula . Pick two points on the line and substitute their x and y values into the formula, then solve. I used the points (-5,-4) and (0,-6):
So, the slope of the line is .
2) Next, use the point-slope formula to write the equation of the line in point-slope form. (From there, we can convert it to slope-intercept form.) Substitute values for the
,
and
into the formula.
Since represents the slope, substitute
in its place. Since
and
represent the x and y values of one point on the line, pick any point on the line (any one is fine, it will equal the same thing at the end) and substitute its x and y values in those places. (I chose (0,-6), as seen below.) Then, with the resulting equation, isolate y to put the equation in slope-intercept form: