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: Recall slope - intercept form

The slope - intercept form of a linear equation is \(y=mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept. We will solve each given equation for \(y\) to get it in this form.

Equation 10: \(2x - y=-1\)

Step2: Solve for \(y\)

Subtract \(2x\) from both sides: \(-y=-2x - 1\)
Multiply both sides by \(- 1\): \(y = 2x+1\)
Slope \(m = 2\), \(y\) - intercept \(b = 1\)

Equation 11: \(3y+2x + 12=0\)

Step3: Solve for \(y\)

Subtract \(2x\) and \(12\) from both sides: \(3y=-2x - 12\)
Divide both sides by \(3\): \(y=-\frac{2}{3}x-4\)
Slope \(m =-\frac{2}{3}\), \(y\) - intercept \(b=-4\)

Equation 12: \(4y + 20=5x\)

Step4: Solve for \(y\)

Subtract \(20\) from both sides: \(4y=5x - 20\)
Divide both sides by \(4\): \(y=\frac{5}{4}x-5\)
Slope \(m=\frac{5}{4}\), \(y\) - intercept \(b = - 5\)

Equation 13: \(3(x - 1)=2x-y\)

Step5: Expand and solve for \(y\)

Expand the left - hand side: \(3x-3 = 2x-y\)
Subtract \(2x\) from both sides: \(x - 3=-y\)
Multiply both sides by \(-1\): \(y=-x + 3\)
Slope \(m=-1\), \(y\) - intercept \(b = 3\)

Equation 14: \(7x-1 = 3y+8\)

Step6: Solve for \(y\)

Subtract \(8\) from both sides: \(7x-9 = 3y\)
Divide both sides by \(3\): \(y=\frac{7}{3}x-3\)
Slope \(m=\frac{7}{3}\), \(y\) - intercept \(b=-3\)

Equation 15: \(9x + 18y=0\)

Step7: Solve for \(y\)

Subtract \(9x\) from both sides: \(18y=-9x\)
Divide both sides by \(18\): \(y=-\frac{1}{2}x\)
Slope \(m =-\frac{1}{2}\), \(y\) - intercept \(b = 0\)

(To graph each line: For the \(y\) - intercept, plot the point \((0,b)\). Then, use the slope \(m=\frac{\text{rise}}{\text{run}}\) to find another point on the line. For example, if \(m = 2=\frac{2}{1}\), from the point \((0,1)\) (for equation 10), rise 2 units and run 1 unit to the right to get the point \((1,3)\), and then draw the line through the two points. After graphing all lines, identify the letter that the graph crosses outside the grid. Since the problem asks to write the letter in the box, but without the actual graph grid, we assume that after graphing each line according to the slope - intercept form, we can find the corresponding letter. However, if we just focus on converting to slope - intercept form, the above steps show how to get each equation in \(y = mx + b\) form.)

Answer:

The equations in slope - intercept form are:

1. \(y = 2x+1\)
2. \(y=-\frac{2}{3}x - 4\)
3. \(y=\frac{5}{4}x-5\)
4. \(y=-x + 3\)
5. \(y=\frac{7}{3}x-3\)
6. \(y=-\frac{1}{2}x\)

(To find the letter, graph each line using the slope and \(y\) - intercept and identify the letter outside the grid that the graph crosses.)