Write the equation of the line that is parallel to 2x – 4y = 8 and passes through the point ( -4, 3) in each of the following forms: point – slope form slope – intercept form standard form

Answers

The point slope form is y - 3 = 1/2(x+4) and the slope intercept form is y = 1/2x + 5.

The Standard form is x - 2y = -10.

Step-by-step explanation:

Parallel lines have the same slope. First, find the slope of the line 2x -4y = 8 by converting it to slope intercept form.

2x - 4y = 8

-4y = 8-2x

y = 1/2x - 2

The slope here is 1/2.

Substitute m = 1/2 and the point (-4,3) into the point slope form. Then simplify to find the Slope Intercept form and standard form.

y -y_1=m(x-x_1)\\y - 3 = \frac{1}{2}(x--4)\\y - 3 = \frac{1}{2}(x+4)\\y - 3 = \frac{1}{2}x + 2\\\\y  = \frac{1}{2}x + 5

The point slope form is y - 3 = 1/2(x+4) and the slope intercept form is y = 1/2x + 5.

Now the standard form can be found by rearranging the terms into the form Ax + By = C.

y= 1/2 x + 5 becomes -1/2x + y = 5. Since standard form cannot have fractions for A or B, multiply the equation by -2.

It becomes x - 2y = -10.

slope-intercept form: y = \frac{1}{2}x+5

point-slope form: (y - 3) = \frac{1}{2}(x + 4)

standard form: x - 2y = -10

Step-by-step explanation:

Lines that are parallel to each other have the same slope.  Using the given line: 2x - 4y = 8, we can solve for slope by converting to slope-intercept form:

-4y = -2x + 8

divide all terms by '-4':  y = \frac{1}{2}x -2

Given a slope of \frac{1}{2} and point of (-4, 3), we can find the three forms:

point-slope form: (y - 3) = \frac{1}{2}(x + 4)

slope-intercept form: y = mx + b or 3 = (\frac{1}{2})(-4) + b

3 = -2 + b or 5 = b, so y = \frac{1}{2}x+5

standard form: x - 2y = -10



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