Final answer:
To find a point satisfying the inequality y > -3x + 1, you can choose x = 0, making a valid point (0, 2). The equation 2x + 3y = 6 can be converted to slope-intercept form y = -2/3x + 2, with a slope of -2/3 and a y-intercept of 2.
Step-by-step explanation:
To find a point that satisfies the inequality y > -3x + 1, you can select any value for x, and calculate the corresponding y value which should be greater than -3x + 1. As an example, if we take x = 0, plugging this into the inequality gives us y > 1. So, a point that satisfies the inequality could be (0, 2), since 2 is greater than 1.
To convert the equation 2x + 3y = 6 into slope-intercept form, we need to solve for y. Subtract 2x from both sides to get 3y = -2x + 6. Then, divide each term by 3 to isolate y, giving us y = -2/3x + 2, which is now in slope-intercept form, y = mx + b, with a slope m of -2/3 and y-intercept b of 2.
The given Figure A1 explains that the slope (denoted as m) and the y-intercept (denoted as b) determine the shape of a straight-line graph. Recalling that a line's slope is constant, and it's calculated by the rise over the run between any two points on the line.