Math

QuestionFind the line with the same slope as the one through (4,1)(-4,-1) and (1,5)(-1,5). Options: y=2y=2, (1,4)(1,4) to (1,6)(1,6), y=12x+5y=\frac{1}{2} x+5, 6x3y=56 x-3 y=5.

Studdy Solution

STEP 1

Assumptions1. The coordinates of the first point are (-4,-1) . The coordinates of the second point are (-1,5)
3. The slope of a line is given by the formulalope=yy1xx1lope = \frac{y - y1}{x - x1}where (x1,y1)(x1, y1) and (x,y)(x, y) are the coordinates of two points on the line.

STEP 2

First, we need to find the slope of the line passing through the points (4,1)(-4,-1) and (1,5)(-1,5). We can do this by substituting the coordinates of these points into the slope formula.
lope=5(1)1(4)lope = \frac{5 - (-1)}{-1 - (-4)}

STEP 3

implify the numerator and the denominator of the fraction.
lope=5+11+lope = \frac{5 +1}{-1 +}

STEP 4

Perform the addition and subtraction operations.
lope=63lope = \frac{6}{3}

STEP 5

implify the fraction to find the slope of the line.
lope=2lope =2

STEP 6

Now that we have the slope of the line, we can compare this with the slopes of the given lines. The line y=2y=2 is a horizontal line with slope0, so it does not have the same slope.

STEP 7

The line passing through (1,4)(1,4) and (1,6)(1,6) is a vertical line with undefined slope, so it does not have the same slope.

STEP 8

The line y=12x+5y=\frac{1}{2} x+5 has a slope of 12\frac{1}{2}, so it does not have the same slope.

STEP 9

The line 6x3y=56 x-3 y=5 can be rewritten in the slope-intercept form y=mx+by=mx+b to find its slope. First, isolate yy on one side of the equation.
3y=6x53y =6x -5

STEP 10

Divide every term by3 to solve for y.
y=2x53y =2x - \frac{5}{3}

STEP 11

From the equation y=x53y =x - \frac{5}{3}, we can see that the slope of the line is, which is the same as the slope of the line passing through the points (4,)(-4,-) and (,5)(-,5).
So, the line 6x3y=56 x-3 y=5 has the same slope as the line passing through (4,)(-4,-) and (,5)(-,5).

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