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HELP

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In the standard (x,y) coordinate plane, a line passes through the points (1,-2) and (5,10). At which of the following points does the line cross the y-axis?

a. (-8,0)

b. (-5,0)

c. (0,0)

d. (0,-8)

e. (0,-5)

Aug 24, 2017
edited by ISmellGood  Aug 24, 2017

#1
+100516
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(1, - 2)   and  (5,10).....we can find the slope  of a line connecttng these points thusly :

[  10 - - 2 ] / [ 5 - 1 ]  =  12 / 4  = 3

The equation of the said line is :

y  = 3 ( x - 5)  + 10

y = 3x - 15 + 10

y = 3x  - 5        where this line crosses the y axis, x  = 0....so

y = 3(0)  - 5   =  0 - 5  =  -5

So.....the line crosses the y axis at  ( 0, - 5)

Here's a graph : https://www.desmos.com/calculator/eearzhfvuk

Aug 24, 2017
#3
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Is the answer a, b, c, or d?

gibsonj338  Aug 24, 2017
#4
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Thanx, I forgot to add the last option haha

ISmellGood  Aug 24, 2017
#2
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To answer the question, first figure out the equaton of the line. To do that first find the slope.  The formula for the slope of a line is

$$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$$ where m = slope, $${y}_{2}$$ = y-coordinate in the second point, $${y}_{1}$$ = y-coordinate in the first point, $${x}_{2}$$ = x-coordinate in the second point, and $${x}_{1}$$ = x-coordintate in the first point.

$$m=\frac{{y}_{2}-{y}_{1}}{{x}_{2}-{x}_{1}}$$

m = ?

$${y}_{2}$$ = 10

$${y}_{1}$$ = -2

$${x}_{2}$$ = 5

$${x}_{1}$$ = 1

$$m=\frac{10-(-2)}{5-1}$$

$$m=\frac{10+2}{5-1}$$

$$m=\frac{12}{5-1}$$

$$m=\frac{12}{4}$$

$$m=\frac{3}{1}$$

$$m=3$$

Now that we know that the slope of the line is 3, put that in the equation for a line.  The equation for a line is

$$y=mx+b$$ where $$y$$ = y-coordinate, $$m$$ = slope, $$x$$ = x-coordinate, and $$b$$ = y intercept (where line crosses the y axis).  Take one of the points and susitute $$x$$ and $$y$$ in the equation so we can solve for b.

$$y=mx+b$$

$$y$$ = 10

$$m$$ = 3

$$x$$ = 5

$$b$$ = ?

$$10=3\times5+b$$

$$10=15+b$$

$$10-15=15+b-15$$

$$-5=15+b-15$$

$$-5=b-0$$

$$-5=b$$

$$b=-5$$

Now fill in what you know leaving $$y$$ and $$x$$ as $$y$$ and $$x$$.

$$y=3x-5$$

To figure out at which point the line crosses the y-axis, subsitute $$x$$ for 0 and solve for $$x$$.

$$y=3x-5$$

$$y=3\times0-5$$

$$y=0-5$$

$$y=-5$$

The point that the line crosses the y-axis is at point $$(0,-5)$$ which means that the answer is neither a, b, c, or d.

Aug 24, 2017