Change to slope-intercept form. Then find the y-intercept, first point, and second point.

Question

-x+3y>6
slope intercept form ______
y-intercept _____
first point (let x=0) ____
second point ______

Answer 1

To convert the inequality \(-x + 3y > 6\) to slope-intercept form (which is \(y = mx + b\)), we start by isolating \(y\).

1. Start with the original inequality: \[ -x + 3y > 6 \]

2. Add \(x\) to both sides: \[ 3y > x + 6 \]

3. Divide every term by \(3\) to solve for \(y\): \[ y > \frac{1}{3}x + 2 \]

Now, the slope-intercept form is: \[ y = \frac{1}{3}x + 2 \] (Note: We typically write the inequality as \(y <\) or \(y >\) depending on the original inequality, but since you asked for slope-intercept, we'll express only the equality part.)

Now let's find the requested values:

Slope-Intercept Form: \[ y = \frac{1}{3}x + 2 \]

y-Intercept: The y-intercept occurs when \(x = 0\): \[ y = \frac{1}{3}(0) + 2 = 2 \]

So, the y-intercept is: \[ (0, 2) \]

First Point (let \(x = 0\)): Using \(x = 0\): \[ y = \frac{1}{3}(0) + 2 = 2 \]

First point is: \[ (0, 2) \]

Second Point (choose another \(x\) value): Let’s choose \(x = 3\): \[ y = \frac{1}{3}(3) + 2 = 1 + 2 = 3 \]

So, another point is: \[ (3, 3) \]

Summary:

• Slope-Intercept Form: \(y = \frac{1}{3}x + 2\)
• Y-Intercept: \( (0, 2) \)
• First Point: \( (0, 2) \)
• Second Point: \( (3, 3) \)