Question

write each equation in slope-intercept form, then use the slope and y-intercept to graph it. the graph will cross a letter outside the grid. write this letter in the box containing the exercise number. 10. 2x - y = -1 12. 4y + 20 = 5x 14. 7x - 1 = 3y + 8 11. 3y + 2x + 12 = 0 13. 3(x - 1) = 2x - y 15. 9x + 18y = 0

Explanation:

Step1: Rewrite in slope - intercept form ($y = mx + b$)

We start with the equation \(2x - y=-1\). We want to solve for \(y\).
Subtract \(2x\) from both sides: \(-y=-2x - 1\).
Multiply both sides by \(- 1\) to get \(y = 2x+1\).

Step2: Identify slope and y - intercept

For the equation \(y = 2x + 1\), the slope \(m = 2\) (which means for every 1 unit we move to the right on the \(x\) - axis, we move up 2 units on the \(y\) - axis) and the \(y\) - intercept \(b = 1\) (the line crosses the \(y\) - axis at the point \((0,1)\)).

Step3: Graph the line

• Plot the \(y\) - intercept \((0,1)\) on the coordinate plane.
• Use the slope to find another point. Since the slope is \(2=\frac{2}{1}\), from the point \((0,1)\), move 1 unit to the right (increase \(x\) by 1) and 2 units up (increase \(y\) by 2) to get the point \((1,3)\).
• Draw a straight line through the points \((0,1)\) and \((1,3)\). When we graph this line, we can see which letter it crosses. From the given grids and the final answer box, when we graph \(y = 2x + 1\), the line will cross the letter \(O\) (corresponding to exercise number 10, and in the bottom box, exercise 10 has the letter \(O\)).

Answer:

For equation \(2x - y=-1\) (exercise 10), the letter is \(O\) (corresponding to the box with exercise number 10, which has the letter \(O\) in the bottom row).