Question

determine 3 solutions to this equation: 4x - 2y = 8.
If the x's that have been given are 0, 2, and negative one, what could be a y for each of them?

Answer 1

Section 1.1 The Coordinate Plane Definition A point P in the coordinate plane is located by a unique ordered pair of numbers (x,y). The number x is called the abscissa (or x-coordinate), and the number y is called the ordinate (or y-coordinate). Examples: Locate the following points in the xy-plane: 1. A(2, 1) ; 2. B(−3, 1) ; 3.C(−2, −4), 4. D(2, −3), 5. E(−3, 0), 6. F (0, −1).
Quadrants
The two axis x and y divide the xy-plane into four regions (or quadrants): Quadrant I is composed of all the points (x,y) such that x > 0 and y > 0, then move counterclockwise to get to quadrant II, where the points (x, y) are such that x < 0 and y > 0, quadrant III where the points (x,y) are such that x < 0 and y < 0, quadrant IV wherethe points (x, y) are such that x > 0 and y < 0.
Distance Formula and Midpoint formula • Let A(x1, y1), and B(x2, y2) rep- resent any two distincts points in the xy-plane. The Euclidean distance between the points A and B can be computed using the formula: d = 􏰨(x2 − x1)2 + (y2 − y1)2 • The coordinates of the midpoint of the points A and B described above are given
by the formula M 􏰦 x1 + x2 ), y1 + y2 􏰧 22
Examples 1. Let A(3, −2), B(−1, 3). Find the distance between points A and B, as well as the coordinates of the midpoint M.
Section 1.2 Lines: Slopes, Equations, Intercepts, Parallel and Perpen- dicular Lines Slope of a Line The Slope m of a line that passes through two points A(x1, y1), and B(x2, y2) is given by
m = rise = y2 − y1 , assuming that x1 ̸= x2. If x1 = x2, then the line is vertical run x2 − x1
(equation: x = x1), and its slope is undefined. Examples: Find the slope of the line that passes through the given points: 1. A(−2, 4) and B(−1, 6) ; 2. A(−2, 4) and B(−2, 7) ; 3. A(−3, 4) and B(0, 4).
The Equation of a Line
• The point-slope form of the equation of a line is given by y−y1 = m(x−x1),
where (x1, y1) is a point on the line and m is the slope of the line.
• The slope-intercept form of the equation of a line is given by y = m x + b,
where m is the slope of the line and b is the y-intercept.
Examples 1. Find an equation of the line that passes through the point (2, −1)
and has slope m = −2. Write the final answer in the format y = mx+b, and in the 3
format Ax + By = C, and graph the line. 2. repeat 1. for the points (−3, −1), and (2,5). 3. Find an equation of the line with slope 2 , and y-intercept −1. Sketch
3
the line. 4. Find the slope and the y-intercept of the line 3x + 7y = −1. Intercepts of Lines
A line with equation Ax + By = C, where A ̸= 0, and B ̸= 0, will intersect both

Answer 2

In simple terms that I could understand, what 3 numbers would be solutions?

Answer 3

substitute the values of x in 4x - 2y = 8. and find y.
(i)4x - 2y = 8
4(0)-2y=8
0-2y=8
0-8=2y
2y=-8
y=-8/2
y=-4
(ii)4x-2y=8
4(2)-2y=8
solve to find y.
(iii)4x-2y=8
4(-1)-2y=8
solve to find y.

Answer 4

can u do t?