Linear EQ, Ratios and Proportions

Front

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

Back

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

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).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

Write the linear equation in slope-intercept form for a line with a slope of 12 and a y-intercept of 10.

Back

y = 12x + 10.

Front

What is a ratio?

Back

A ratio is a comparison between two quantities, showing how many times one value contains or is contained within the other.

Front

If the ratio of a to b is 3:4, what is the value of a if b = 8?

Back

If b = 8, then a = (3/4) * 8 = 6.

Front

What is the relationship between ratios and proportions?

Back

A proportion states that two ratios are equal. For example, if a/b = c/d, then a:b is proportional to c:d.

Front

How do you solve for x in the equation 2x + 3 = 7?

Back

To solve for x, subtract 3 from both sides to get 2x = 4, then divide by 2 to find x = 2.

Front

What is the graphical representation of the equation y = -\frac{2}{3}x + 4?

Back

The graph is a straight line with a slope of -\frac{2}{3} and a y-intercept of 4.

Front

What does it mean for two lines to be parallel?

Back

Two lines are parallel if they have the same slope and will never intersect.