Write the equation of the line in slope-intercept form that goes through the points: (0, 3) and (3, -6)

y = -3x + 3  

Step-by-step explanation:

Slope-intercept form is represented by the equation y = mx + b. We can write an equation in point-slope form first, then convert it to that form.  

1) First, find the slope of the equation. Use the slope formula and substitute the x and y values of the given points into it. Then, simplify:

Thus, the slope is -3.

2) Now, use the point-slope formula, and substitute values for , , and . From there, we can isolate y to convert the equation into slope-intercept form.

Since represents the slope, substitute -3 in its place. Since and represent the x and y values of one point the line intersects, choose any one of the given points (either one is fine) and substitute its x and y values into the formula, too. (I chose (0,3), as shown below). Finally, isolate y to find the

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.

step-by-step explanation: