math algebra cordinate ?s?

Question

For problems #4 through #6, find the x- and y-intercepts for each equation. Write your answers as ordered pairs.

4) 3x + 9y = 15

5) –4x – 3y = 21

6) 2x – 7y = 14

For problems #12 through #16, write the equation of a line in slope-intercept form for the given situations

13) passing through (2, -3) and (-1, -9)

35) Solve –3(2x + 1) + 4(x – 2) = x + 1

36) Solve 7x – 3(x + 2) > 6.

Answer 1

For problems 4-6. To find the y-intercept set x = 0. Then
solve for y.
(You set x = 0, because the y- axis is vertical and is the line x =0)
To find the x-intercept, set y = 0. Then solve for x.

For problems 12-16.

A line in slope intercept form is given as follows
y = mx+ b (where m is the slope and b is the y-intercept)

To find the slope use the formula (y2-y1)/(x2-x1)
Then find the y-intercept.
To find the y-intercept of your line equation, use 1 of the coordinate sets (x,y) that you are given and put the x-value
and y-value into the equation to find b.

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For example

Find a line passing through (5,1) and (3,2)

slope (y2-y1)/(x2-x1) = (1-2)/(5-3)
= -1/2
m= -1/2

Slope intercept form (line) : y=mx+b

I will substitute values from the (3,2) coordinate pair.

3 = (-1/2)(2) + b
b = 1
So the line in Slope intercept form is
y= -1/2(x) + 1