Exercises: Slope, Similar Triangles, and Linear Equations

Which of the following describes a slope triangle for a line?

Two triangles are similar. Their corresponding sides are in the ratio 1 : 3. If the shorter triangle has a vertical leg of 4 and a horizontal leg of 6, what is the horizontal leg of the larger triangle?

A line passes through the origin $(0, 0)$ and the point $(3, 6)$. What is the slope of the line?

A line passes through the origin and has slope $3$. What is the $y$-value when $x = 4$? Use the equation $y = mx$.

Two slope triangles are drawn on the same line. The smaller triangle has rise $= 2$ and run $= 3$. The larger triangle has rise $= 4$. What is the run of the larger triangle? (The triangles are similar.)

A line passes through the origin and the point $(2, 5)$. Write the equation of the line in the form $y = mx$. Enter the value of $m$ as a fraction.

A line has slope $2$ and $y$-intercept $(0, 1)$. Using the equation $y = mx + b$, what is the $y$-value when $x = 3$?

The equation of a line is $y = -3x + 4$. What are the slope and $y$-intercept?