Mathematics, 30.08.2019 06:00 sydneyrasmussen

Line "m" has intercepts (7,0) and (0, -2)
what is the equation of line "m"?
is the point (49, -16) also on line "m"? how do you know?

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The equation of a line is usually written in what's called slope-intercept form.

Slope-intercept form is written as y = mx + b where m = slope and b = the y-intercept.

The slope of a line can easily be found just by using two points on the line. The slope is equal to the rise over the run, or the difference in y over the difference in x, between the two points.

$slope = \frac{y_2-y_1}{x_2-x_1} = \frac{-2-0}{0-7} = \frac{-2}{-7} = \boxed{\frac{2}{7}=m}$

The y-intercept of the line is the point at which it intersects the y-axis. (The vertical axis.) All points on the y-axis have an x coordinate of 0, so we would then add or subtract the rise and run to a point on the line until we reached x = 0.

Fortunately, we already have this point! It's (0, -2)!

$y-intercept=\boxed{-2=b}$

Now we just need to put our slope and y-intercept into the equation.

$\boxed{\boxed{y=\frac{2}{7}x-2}}$

And to test if a point is on this line, just plug in the x and y coordinates and see if the equation is true!

$-16 = \frac{2}{7}*49-2 \\ -16 = 14 - 2 \\ -16 \neq 12,\ \therefore line\ m\ does\ not\ contain\ (49, -16)$

Answer from: Quest

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.

Answer from: Quest

need more detail

step-by-step explanation:

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