How do you graph the inequality $$5x - 8 \leq 7$$ ?

First, solve for x: $$5x \leq 15$$ , so $$x \leq 3$$ . Then, graph a solid line at x = 3 and shade to the left.

Evaluate the expression $$-3x^2 - 5x + 7$$ when x = -2.

Substituting x = -2 gives: $$-3(-2)^2 - 5(-2) + 7 = -3(4) + 10 + 7 = -12 + 10 + 7 = 5$$ .

How do you convert the standard form of a linear equation to slope-intercept form?

To convert $$Ax + By = C$$ to slope-intercept form, solve for y: $$y = -\frac{A}{B}x + \frac{C}{B}$$ .

What is the significance of the y-intercept in a graph?

The y-intercept is the point where the graph crosses the y-axis, indicating the value of y when x = 0.

What is the solution set of the inequality $$x + 3 > 5$$ ?

The solution set is $$x > 2$$ .

How do you determine if a point (x, y) lies on the line represented by the equation $$y = 2x + 1$$ ?

Substitute the x-value into the equation and see if the resulting y-value matches the y-coordinate of the point.

What is the formula for the slope between two points?

The formula for the slope (m) between two points (x1, y1) and (x2, y2) is $$m = \frac{y2 - y1}{x2 - x1}$$ .

What does it mean for a function to be linear?

A function is linear if it can be represented by a straight line on a graph, meaning it has a constant rate of change.

How do you find the x-intercept of the equation $$y = 4x + 2$$ ?

Set y = 0 and solve for x: $$0 = 4x + 2$$ , which gives $$x = -\frac{1}{2}$$ .

What is the graphical representation of the equation $$y = 4x + 2$$ ?

It is a straight line with a slope of 4 and a y-intercept of 2.

Flashcard

•

Mathematics

•

10th Grade

•

Practice Problem

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Hard

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CCSS

8.F.A.3, 8.EE.B.5, 6.EE.B.8

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

FLASHCARD QUESTION

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Tags

CCSS.8.EE.B.5

FLASHCARD QUESTION

Front

Back

The y-intercept is 4, which is the value of f(0).

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

FLASHCARD QUESTION

Front

Back

Tags

CCSS.6.EE.B.8

FLASHCARD QUESTION

Front

Back

Tags

CCSS.6.EE.A.2C

FLASHCARD QUESTION

Front

Back

The slope is -1, as it is the coefficient of x in the slope-intercept form.

Tags

CCSS.8.EE.B.5

FLASHCARD QUESTION

Front

What does the term 'linear equation' mean?

Back

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