Question

use your understanding of graphing linear equations to answer the question below. 11. mrs. schultz asked her students how they would graph the linear equation below. first, graph the line on the provided coordinate grid. then, read the discussion from the students and circle any statements that are true. y = 2x + 1 maxwell first, i would plot the y - intercept at (1, 0). eleanor from the y - intercept, i would count up two and to the right one and plot a point at (1, 3). dylan from the y - intercept, i would count down two and to the left one and plot a point at (-1, -1).

Explanation:

Step1: Recall y - intercept formula

For a linear equation $y = mx + b$, the y - intercept is at the point $(0,b)$. In the equation $y=2x + 1$, $b = 1$, so the y - intercept is at $(0,1)$, not $(1,0)$ as Maxwell said. So Maxwell's statement is false.

Step2: Recall slope - based point - plotting

The slope $m$ of the line $y=2x + 1$ is $m = 2=\frac{2}{1}$. Starting from the y - intercept $(0,1)$, if we move up 2 units (rise) and right 1 unit (run) according to the slope, the new point is $(0 + 1,1+2)=(1,3)$. So Eleanor's statement is true.

Step3: Use negative slope interpretation

The slope $m = 2$. If we consider the negative direction of the slope, moving down 2 units and left 1 unit from the y - intercept $(0,1)$, we get the point $(0-1,1 - 2)=(-1,-1)$. So Dylan's statement is true.

Answer:

Eleanor's statement is true. Dylan's statement is true. Maxwell's statement is false.