Question

writing equations for lines
use slopes to describe the relationship between points on a line and the slope of the line

match each line shown with a slope from this list:
$\frac{1}{3}$__ 2 $\frac{7}{5}$__
1__ 0.25 $\frac{3}{2}$__
one of the given slopes does not have a line to match. draw a line with this slope on the empty grid (f).

Explanation:

Step1: Recall slope formula

The slope $m$ of a line is given by $m=\frac{\text{rise}}{\text{run}}$, where rise is the vertical change and run is the horizontal change between two points on the line.

Step2: Analyze slopes visually

For a slope of $\frac{1}{3}$, the line has a gentle upward - slant. For a slope of 2, the line is quite steep going upwards. For a slope of $\frac{11}{6}\approx1.83$, it is also a steep upward - slanting line. For a slope of 1, the line makes a 45 - degree angle with the horizontal. For a slope of 0.25, it is a very gently upward - slanting line. For a slope of $\frac{3}{2} = 1.5$, it is a moderately steep upward - slanting line.

Step3: Match slopes to lines

Match the slopes to the lines based on their steepness and upward - slant.

Answer:

1. Match the slopes to the lines:

• $\frac{1}{3}$: Matches a line with a gentle upward - slant.
• 2: Matches a steep upward - slanting line.
• $\frac{11}{6}$: Matches a steep upward - slanting line.
• 1: Matches a line at a 45 - degree angle.
• 0.25: Matches a very gently upward - slanting line.
• $\frac{3}{2}$: Matches a moderately steep upward - slanting line.

1. Identify the unmatched slope and draw the line

• First, determine which slope is unmatched by comparing the visual steepness of the given lines. Then, on the empty grid, start at a point, and for a slope $m=\frac{\text{rise}}{\text{run}}$, from the starting point, move the number of units up (rise) and right (run) according to the values of rise and run in the slope fraction to draw the line. For example, if the unmatched slope is $\frac{1}{3}$, from a starting point $(x_0,y_0)$, move 1 unit up and 3 units right to get another point $(x_0 + 3,y_0+1)$ and draw the line passing through these two points.