Question

AlgebraSHOW ALL WORKGiven the points (6,-4) and (0,4), find the slope, the y-intercept, and the x-intercept of the line that passes through both point. Also, GRAPH this line

Answer 1

Answer:

• slope: -4/3
• y-intercept: (0, 4)
• x-intercept: (3, 0)
• y = -4/3x +4

Step-by-step explanation:

Given two points, the equation for the line through them can be found using the slope formula and the slope-intercept form.

The slope formula is ...

  m = (y2 -y1)/(x2 -x1)

  m = (4 -(-4))/(0 -6) = 8/-6 = -4/3 . . . . slope of the line

The y-intercept is 4, given by the second point.

The slope-intercept equation for a line is ...

  y = mx +b . . . . . . line with slope m and y-intercept b

  y = -4/3x +4 . . . . . line with slope -4/3 and y-intercept 4

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The x-intercept can be found by solving for x when y=0.

  0 = -4/3x +4

  0 = 4x -12 . . . . multiply by -3

  0 = x -3 . . . . . . divide by 4

  3 = x . . . . . . . . subtract 3

The x-intercept is (3, 0).

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The line can be graphed by plotting the given points and drawing the line through them.

Answer 2

Answer:

Slope: $-\frac{4}{3}$

Y int. : (0,4)

X int. : (3,0)

Step-by-step explanation:

Equations to remember:

$y = mx + b\\\\\frac{y_{2}-y_{1} }{x_{2}-x_{1}}$

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$(x_{1}, y_{1}) = (6, -4)\\\\(x_{2}, y_{2}) = (0,4)$

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SLOPE

You want to set up your equation for finding slope like this:

$\frac{4 - (-4)}{0 - 6}$

4 - (-4) will become 4 + 4. This is because there is a -1 in front of the parenthesis.

A negative number times a negative number will always equal a positive number.

$-\frac{8}{6}$

when simplified/divided by 2, which is the number you want:

$-\frac{4}{3}$

This is your slope or your m in y = mx + b

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Y INTERCEPT

Use one of your points.

I'll use (0,4) as an example.

Set up your equation like this:

$4 = -\frac{4}{3}(0) + b$

Since your slope is being multiplied by ZERO, you can just eliminate your mx or slope.

This means that 4 = b!

That's your Y Int, which you'll find was one of the given points, (0,4).

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From there, if you use a graph, you should find that your X Int is (3,0).

I hope this helped you!