Question

Please help me

Part A.) In the coordinate plane below, triangle LMN is similar to triangle RST. What is the slope of LN? Justify your answer.

Part B.) Write an equation that represents line c. Show work or explain how you determined the equation.

Answer 1

A: 4/3x B: 3/4x + 7

Explanation:

Part A: Since LN shares the same line as RT, they will have the same slope.

R coord (4, 10)

T coord (12, 16)

Rise over run will get you 4/3x as the slope.

Part B: The line can be represented using y = mx+b

If we go back one place value from (4, 10), we get (0, 7). Making 7 our b. Since we got the slope from part A, all we have to do now is plug in.

Line C: 3/4x + 7

Answer 2

A)

Because it uses the same line as RT, then you can get LN's slope by getting RT's slope.

Equation: (y₂ - y₁)/(x₂ - x₁)

Our case: (16-10)/(12-4) = 6/8 = 3/4

B)

Point-slope formula: y - y₁ = m(x - x₁)

We already have m, it's the slope. And we can choose whichever point from our graph, I'm gonna choose (4, 10)

Our case: y - 10 = 3/4(x - 4)

y - 10 = (3/4)x - 4(3/4)

y - 10 = (3/4)x - 3

y = (3/4)x + 7