Solve for y intercepts

7x+y=-2
Answer: Y = -2

7x + 2y = 4
Answer: Y = 2
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If (3,-5) is a point on the graph for the equation in the form y=mx+7, then m=?

Answer:
-5=m(3)=7
m=-4
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Identify slope and y - intercept
y=7x+3
Answer: slope=7 y intercept=3

4x-y =0
Ans: slope =4 y intercept = 0
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Solve for r
(1,r) (3,-5) are two points on a line with slope -4.
Find r
Answer:
r = (-5 - r)/( 3-1 )
r= 3
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Write the slope intercept for of the equation:
>slope = -5/4 , y intercept = -4
Ans: y = -5/4x - 4

>Through (-1,4), slope = -2
Ans: y = -2x +2

>Through (4,2) and (0,4)
Ans y= 1/2x -4
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Write the slope intercept form of the equation of the line described:
Through (-1,2), parallel to y = -x - 1

Answer: y = -x + 1
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all look good except this one:

>Through (4,2) and (0,4)
Ans y= 1/2x -4

from given: y = mx + 4
plug in the given point:
2 = 4m + 4
-2 = 4m
m = -1/2

so y = (-1/2)x + 4

notice both (4,2) and (0,4) satisfy my equation.

To solve for y-intercepts in an equation, you can set x to 0 and solve for y. The y-intercept is the value of y when x is 0.

For the equation 7x + y = -2:
Set x to 0:
7(0) + y = -2
y = -2

So the y-intercept is y = -2.

For the equation 7x + 2y = 4:
Set x to 0:
7(0) + 2y = 4
2y = 4
y = 2

So the y-intercept is y = 2.

To find the slope (m) in the equation y = mx + 7 when a point (3, -5) is on the graph, you need to substitute the x and y values and solve for m.

The equation y = mx + 7 can be rewritten as -5 = m(3) + 7.

-5 = 3m + 7
-12 = 3m
m = -4

So the value of m is -4.

For the equation y = 7x + 3:
The slope (m) is 7 and the y-intercept is 3.

For the equation 4x - y = 0:
The slope (m) is 4 and the y-intercept is 0.

To solve for r in the equation with two points (1, r) and (3, -5) and a slope of -4, you can use the slope formula: (y2 - y1) / (x2 - x1) = -4.

Substituting the coordinates (1, r) and (3, -5):
(-5 - r) / (3 - 1) = -4
(-5 - r) / 2 = -4
-5 - r = -8
r = 3

So the value of r is 3.

To write the slope-intercept form of an equation (y = mx + b) given the slope and y-intercept:
For example, if slope (m) is -5/4 and the y-intercept (b) is -4, the equation would be:
y = (-5/4)x - 4

If the slope is -2 and the point (-1, 4) is on the line, you can substitute the values into the equation and solve for y:
4 = -2(-1) + b
4 = 2 + b
b = 2
So the equation is y = -2x + 2.

If the line passes through the points (4, 2) and (0, 4), you can use the slope formula to find the slope (m):
m = (y2 - y1) / (x2 - x1)
m = (4 - 2) / (0 - 4)
m = 2 / (-4)
m = -1/2

Using the slope-intercept form, y = mx + b, and substituting any of the given points, you can solve for the y-intercept (b):
2 = (-1/2)(4) + b
2 = -2 + b
b = 4

So the equation is y = (-1/2)x + 4.

To write the slope-intercept form of a line parallel to y = -x - 1 and passing through the point (-1, 2), you know that the slope of the parallel line will be the same. So the slope is -1. Substituting this slope and the given point (-1, 2) into the slope-intercept form, you can solve for the y-intercept:
2 = -1(-1) + b
2 = 1 + b
b = 1

So the equation is y = -x + 1.