what is the equation of the line that contains the point with (x,y) coordinate?

Question

(-3,7) and (5, 7)?

Answer 1

If you graph those points you'll see that you have a horizontal line because the y coordinate does not change. So that would just be y = 7.
Ordinarily you'd find the slope and then put this in the point slope formula but since the slope of this one is 0 you wouldn't do it that way, you'd have to recognise that horizontal lines have the form y = a constant and vertical lines have the form x = a constant

Answer 2

Objectives:
1.To write the equation of a lines using the
Slope-Intercept Formula.
2.To write the equation of a lines using the
Point-Slope Formula.

For the equation y = mx + b we know that the slope is m and the y-intercept is b. We can draw the graph by using the slope and y-intercept. If enough is known about the non-vertical line, a sketch of the graph could be completed, and the model y = mx + b can be used to write the equation of a line.

Slope-Intercept Form (y = mx + b)
Write the equation of the line given its slope and
y-intercept.
Given: m = -2 and b = 3
Y = mx + b
Y = -2x + 3

Write the equation of a line given the slope and one point.
Using the Point-slope Formula.
P(-2,3) and slope is 4
Y = mx + bThe equation of the line:
3 = 4(-2) + by = 4x = 11
3 = -8 + b
-11 = b
Point-Slope Formula can be used to write the equation of a line given a point and the slope or given two points.

Point-Slope Formula
Given:P(x, y) represents any point on a line.
Q(x1 , y1 ) represents a given point on the line.
Find the slope using the slope formula.

Write an equation of a line given the slope and a point using the Point-slope Formula.
P(-3,-4) Slope is -2/3
y - y1 = m(x - x1 )


Write an equation of a line given 2 points.
P(2,3) and Q(-3, - 5)
Use the Point-Slope Formula:y - y1 = m(x - x1 )

Find the slope:
y - y1 = m(x - x1 )


Special Cases
Y = b Horizontal Line, m = 0.
X = cVertical Line, m is undefined.

Write an equation of a line whose slope is 0 and contains the point P(3, - 5).
Since the slope is 0, this is a horizontal line. Equation is of the form y = b, where b is the
y-coordinate of the point P(3, -5). So the equation of the line is y = -5.

Write an equation of a line containing the points C(4, -2) and D(4, 5).

Because the x-coordinates of points C and D are the same, this is a vertical line. Therefore, the equation is of the form x = c, where c is the x-coordinate. So the equation is x = 4.
Analyzing Conditions
Sometimes a line is described in reference to one or more other lines.
68.The equation of L2 is 2x - 3y = 1. L1 is perpen-
dicular to L2 , and its y-intercept is (0, -4).
Slope of L2 :3y = 2x - 1;
Slope of L1 is -3/2 Point on L1 P(0, -4)

78.The line 3y + 2kx - 8 = 0 is parallel to a line
y = -2 + x. Find k.
Slope of the line whose equation is y = -2 + x is 1.
Slope of the line whose equation is 3y + 2kx - 8 = 0 is
Solve 3y +2kx - 8 = 0 for y.)
3y +2kx - 8 = 0; 3y = -2kx + 8; y=-2kx/3+8/3

So

82.The line 3x -5y - k = 0 has the same y-intercept as y = 2-4x. Find k.

Y-intercept of the line whose equation is
y = 2 - 4x is 2.

Find the y-intercept of the graph whose equation is
3x -5y - k = 0.
-5y = k - 3x
The y-intercept is .

So

Answer 3

y=7