Question

1. sally and ray work together on an assignment. they have broken down the work into 4 parts of the same size. sally works at 2 times the speed of ray but has 5 pieces of work to do for another subject. this problem can be represented by the following system of equations: equation 1: $x + y = 4$ equation 2: $y = 2x - 5$ 6a sketch the two lines representing these equations on the graph below: graph with x and y axes, grid, and some blue points plotted

Explanation:

Step1: Analyze Equation 1 ($x + y = 4$)

Rewrite it in slope - intercept form ($y=mx + b$), where $m$ is the slope and $b$ is the y - intercept. We get $y=-x + 4$. The slope $m=- 1$ and the y - intercept $b = 4$. To find two points on this line, when $x = 0$, $y=4$; when $y = 0$, $x = 4$.

Step2: Analyze Equation 2 ($y=2x - 5$)

This is already in slope - intercept form. The slope $m = 2$ and the y - intercept $b=-5$. To find two points on this line, when $x = 0$, $y=-5$; when $x=\frac{5}{2}$, $y = 0$.

Step3: Sketch the lines

For $y=-x + 4$, plot the points $(0,4)$ and $(4,0)$ and draw a straight line through them. For $y = 2x-5$, plot the points $(0,-5)$ and $(\frac{5}{2},0)$ and draw a straight line through them. (In the given graph, we can also use the existing points: for $x + y=4$, when $x = 1$, $y = 3$; when $x = 2$, $y = 2$ etc. For $y=2x - 5$, when $x = 2$, $y=-1$; when $x = 3$, $y = 1$ etc. to sketch the lines accurately.)

(Note: Since the question is about sketching the lines, the final answer is the graphical representation of the two lines $y=-x + 4$ and $y = 2x-5$ on the given coordinate plane. If we were to describe the lines: One line has a slope of - 1 and y - intercept 4, the other has a slope of 2 and y - intercept - 5.)

Answer:

The two lines are: one with equation $y=-x + 4$ (slope - 1, y - intercept 4) and one with equation $y = 2x-5$ (slope 2, y - intercept - 5) sketched on the given coordinate plane.