Me determine the equation of the line in slope intercept form and show all work. a line that is perpendicular to the line
y = (1/2)x + 10 that passes through the
point (50,60).

y=-2x+160

Step by Step:

The equation of a line can be determined using the point slope formula:

y-y1=m (x-x1)

To make a substitution, we must ensure we have the correct information. The question gives:

y1=60

x1=50

y=1/2x+10 This is the formula of a line that is perpendicular to the one we are trying to find.

It tells us that the gradient of the perpendicular line is 1/2. The gradient of the line we are trying to find can be found using m1×m2=-1 because we know that when lines are perpendicular, the product of their gradients must equal 1

So if we replace m1 with 1/2

1/2×m2=-1

m2=-2

We now have all the relevant information to make a substitution:

y-60=-2 (x-50)

expand brackets

y-60=-2x+100

rearrange to get in the form y=mx+b

y=-2x+160

shift 4 units up, and 1 unit left.

it will translate f(x) = 3^x to g(x) = 3^(x+1) + 4

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.