A line and a right triangle are shown in the graph below.

Question

Graph shows a line passing through the origin. A right triangle formed on first quadrant has a vertex at (0, 0), base on x-axis, and hypotenuse on the line. The base measures 7 units and height 4 units.

What is the equation of the line?

A. y = 4/7x




B. y= 4x+7

C. y= 7/4x




D. 7x + 4

Answer 1

To determine the equation of the line that forms the hypotenuse of the right triangle, we need to use the coordinates of the points that define the triangle.

The triangle has one vertex at the origin $(0,0)$, a base that goes along the x-axis (from $(0,0)$ to $(7,0)$), and a height that goes up to the line at the point $(7,4)$.

The slope $m$ of the line that goes through these two points $(0,0)$ and $(7,4)$ can be calculated using the formula for the slope: $$m=\frac{\text{change in y}}{\text{change in x}}=\frac{4-0}{7-0}=\frac{4}{7}$$

Using the slope-intercept form $y=mx+b$, and since the line passes through the origin, the y-intercept $b=0$. Thus, the equation of the line becomes: $$y=\frac{4}{7}x$$

The correct answer is: A. y = \frac{4}{7}x.