Question

1. in the graph below, triangles jhi and mlk are right triangles, and points i, k, j and m all lie on a straight line. which statement is true about the graph? a. the absolute value of the slope of the line is $\frac{ml}{jh}$. b. the measure of angle l is less than the measure of angle h. c. the absolute value of the slope of the line is equal to $\frac{ih}{hj}$. d. the absolute value of the slope of the line is equal to $\frac{\frac{ih}{hj}}{\frac{kl}{ml}}$. 4. if you were to graph a line with a slope of $\frac{3}{2}$ that intercepts the y - axis at - 2 on the coordinate plane, one point on that line would have a y coordinate of 4 with an x coordinate of what number?

Explanation:

3.

Step1: Recall slope formula

The slope $m$ of a line is given by $m=\frac{\text{rise}}{\text{run}}$. For two right - triangles formed by a line, the ratio of the vertical side to the horizontal side of either triangle gives the slope of the line. In right - triangles $JHI$ and $MLK$, the slope of the line is $\frac{ML}{LK}=\frac{IH}{JH}$. The absolute value of the slope of the line is the ratio of the length of the vertical side to the length of the horizontal side of the right - triangle formed by the line on the coordinate plane.

Step2: Analyze each option

• Option A: The absolute value of the slope of the line is $\frac{ML}{LK}$ (not $\frac{ML}{JH}$), so A is incorrect.
• Option B: Since the two triangles are similar (because they are formed by the same line and are right - triangles), the corresponding angles are equal. So $\angle L=\angle H$, and B is incorrect.
• Option C: The absolute value of the slope of the line is $\frac{IH}{JH}=\frac{ML}{LK}$, so C is correct.
• Option D: $\frac{IH}{JH}

eq\frac{\frac{IH}{JH}}{\frac{ML}{LK}}$, so D is incorrect.

Step1: Write the equation of the line

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. Given $m=\frac{3}{2}$ and $b=-2$, the equation of the line is $y=\frac{3}{2}x - 2$.

Step2: Substitute the y - value and solve for x

We are given $y = 4$. Substitute $y = 4$ into the equation $y=\frac{3}{2}x - 2$:
\[

$$\begin{align*} 4&=\frac{3}{2}x-2\\ 4 + 2&=\frac{3}{2}x\\ 6&=\frac{3}{2}x\\ x&=6\times\frac{2}{3}\\ x&=4 \end{align*}$$

\]

Answer:

C. The absolute value of the slope of the line is equal to $\frac{IH}{JH}$

4.