The Slope of a Line The slope of a line is the ratio of the vertical distance to the horizontal distance of a slope triangle formed by two points on a line. The vertical part of the triangle is called y (Δy ) (read “change in y”), while the horizontal part of the triangle is called x (Δx ) (read “change in x”). It indicates both how steep the line is and its direction, upward or downward, left to right. Note that lines pointing upward from left to right have positive slope, while lines pointing downward from left to right have negative slope. A horizontal line has zero slope, while a vertical line has undefined slope. To calculate the slope of a line, pick two points on the line, draw a slope triangle (as shown in the example at Right), determine Δy and Δx, and then write the slope ratio. You can verify that your slope correctly resulted in a negative or positive value based on its direction. In the example above, Δy = 2 and Δx = 5, so the slope is 2/5 .
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- 2-41. If y = 1/2x − 4: 2-41 HW eTool (Desmos).
- What is the slope of the line?
- What is the y‑intercept of the line?
- Graph the line.
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Writing Linear Equations from Slope and/or Points You can find the equation of a line when you know the slope and one point on the line. To do so, rewrite y = mx + b with the known slope and substitute the coordinates of the known point for x and y. Then solve for b and write the new equation. For example, find the equation of the line with a slope of –4 that passes through the point (5, 30). Rewrite y = mx + b as y =–4x + b. Substituting (5, 30) into the equation results in 30 = –4(5) + b. Solve the equation to find b = 50. Since you now know the slope and y‑intercept of the line, you can write the equation of the line as y = –4x + 50. |
Graphing the Line Maze Challenge