Summary: Forms of Two-Variable Linear Equations

Which of the following is the standard form of a linear equation?

• y=mx+b

• Ax+By=C

• y=ax²+bx+c

• y-y₁=m(x-x₁)

Answer explanation

The standard form of a linear equation is Ax + By = C, where A, B, and C are constants. The other options represent different forms of linear equations or quadratic equations.

In the equation 2y+1= 16x-2, what is the slope?

• 8

• 10

• 5

• -7

Answer explanation

To find the slope, rearrange the equation to slope-intercept form (y = mx + b). Starting with 2y + 1 = 16x - 2, we get 2y = 16x - 3, then y = 8x - 1. The slope (m) is 8.

What is 2(y+3)=10x in slope-intercept form?

• y=15x-4

• y=6x+5

• y=5x-6

• y=5x/4

Answer explanation

To convert 2(y+3)=10x to slope-intercept form, first distribute: 2y + 6 = 10x. Then, isolate y: 2y = 10x - 6, so y = 5x - 3. The correct answer is y = 5x - 6, which matches the given options.

What is the definition of y-intercept?

• The maximum y value

• Where the line crosses the y-axis at x=0

• Where the line crosses the x-axis at y=0

• Slope of the line

Answer explanation

The y-intercept is defined as the point where a line crosses the y-axis, which occurs when x=0. This means the correct choice is 'Where the line crosses the y-axis at x=0', as it accurately describes the y-intercept.

Find the slope of the line in the picture shown.

• 4/3

• 5

• 3/4

• -4

Answer explanation

To find the slope, use the formula (change in y) / (change in x). If the line rises 4 units for every 3 units it runs, the slope is 4/3. Thus, the correct answer is 4/3.

What is the slope intercept form for the line shown?

• y=4x+5

• y=7x-5

• y=5x+3

• y=2x+5

Answer explanation

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. The correct choice, y = 2x + 5, has a slope of 2 and a y-intercept of 5, matching the line shown.

What does point-slope form show?

• It shows the slope only

• It shows the slope and a point on the line

• It shows the slope and the y-intercept

• It shows only the y-intercept

Answer explanation

Point-slope form represents a linear equation using the slope and a specific point on the line. This allows you to easily graph the line or find other points on it, making the correct choice "It shows the slope and a point on the line."

What can you say about a line with a slope of 0?

• The line is decreasing

• The line is increasing

• The line is horizontal

• The line is verticle

Answer explanation

A line with a slope of 0 indicates that there is no vertical change as you move along the line, meaning it remains constant. Therefore, the line is horizontal.

What is point slope form?

• Ax+By=C

• • y=mx+b

• y²=4px

• y-y₁=m(x-x₁)

Answer explanation

Point slope form is represented by the equation y - y₁ = m(x - x₁), where m is the slope and (x₁, y₁) is a point on the line. This form is useful for writing the equation of a line when you know its slope and a point.

What equation is parallel to the line in the photo?

• y=4x/5+7

• y=5x/4+1

• y=5x+2

• y=x+5

Answer explanation

The correct choice, y=4x/5+7, has the same slope as the line in the photo, which is 4/5. Parallel lines share the same slope, making this equation the only one that is parallel to the given line.