Tell whether the lines y=-4x+3 and -2x+8y=5 are parallel, perpendicular, or neither.

The lines are perpendicular to each other.

Step-by-step explanation:

Given equations of lines:

1.

2.

Writing equation both equations in slope-intercept form which is

where represents slope and represents y-intercept.

1.

This is already in slope-intercept form.

The slope of the line

2.

Adding both sides.

Dividing both sides by 8.

Splitting denominators.

Simplifying fraction.

So, for the line the slope is.

A) Checking for parallel.

For parallel lines the slopes of the line are equal.

Since

So, lines are not parallel.

B) Checking for perpendicular.

For perpendicular line the slopes of the line are related as:

Finding the product of the slopes to check weather it equals -1.

⇒

The condition for perpendicular lines is satisfied as the product of the slopes =-1

Hence, the lines are perpendicular to each other.

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

step-by-step explanation:

ratios represent a pattern or relationship that can be scaled.

equivalent ratios are pairs of ratios that represent the same relationship between quantities, and can be generated by multiplying or dividing both quantities in the ratio by the same factor.

in this lesson, students will use double number lines and ratio reasoning to solve ratio problems. by partitioning double number lines into proportionate intervals, students will build an understanding of equivalent ratio relationships as those that are generated by multiplying or dividing two related quantities by the same number. this lesson will build upon students' prior understanding of multiplicative comparisons, number line reasoning and equivalent fractions (while highlighting the difference between equivalent fractions and equivalent ratios); and will build toward future work in this unit on building ratio tables, and work in future grades in proportionality, scaling, and expressing and graphing linear functions.

27 + 13x + 15 = (x + 5)( =

step-by-step explanation:

27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( = 27 + 13x + 15 = (x + 5)( =