straight line

**decoy808** · November 30th 2009, 02:31 AM

a straight line equation y=4x-5

i found the xy intercept

(5/4, -5)

question (a) find a line that is perpendicular and passes the point (1,2)
quesiton (b) at what coordinates do the lines cross.

is there a way to find by calculation? or do i just draw the lines?

many thanks

**user_5** · November 30th 2009, 02:58 AM

For a perpendicular line, you need $m_1*m_2=-1$

$m_1$ represents the gradient of the original equation and $m_2$ represents the gradient of the perpendicular line.

$4*m_2=-1$
$m_2=-\frac{1}{4}$

Therefore the gradient of your perpendicular line is $-\frac{1}{4}$

$y=mx+c$
$y=-\frac{1}{4}x+c$

Sub in the point they give you (1,2) and solve for c.

$2=-\frac{1}{4}(1)+c$

Can you continue from here?

To find the intersection of the two graphs, let the two equations equal each other.

**HallsofIvy** · November 30th 2009, 02:58 AM

Originally Posted by decoy808

a straight line equation y=4x-5

i found the xy intercept

(5/4, -5)

What do you mean by "xy intercept"? The "x-intercept" is the point where the line crosses the x-axis; where y= 0 so x= 5/4 and the point is (5/4, 0). The "y-intercept is the point where the line crosses the y-axis: where x= 0 so y= -5 and the point is (0, -5). But I have never heard of an "xy intercept" and the point (5/4, 5) is not on this line.

question (a) find a line that is perpendicular and passes the point (1,2)

Use the fact that if y= mx+ b and y= nx+ b are perpendicular then mn= -1.
Your first line has slope 4 so you are looking for the equation of the line through (1, 2) with slope -1/4

quesiton (b) at what coordinates do the lines cross.

is there a way to find by calculation? or do i just draw the lines?

many thanks

Solve the two equations simultaneously. If you have them in the form y= mx+ a and y= nx+ b, the first step is easy: subtract one of the equations from the other and the "y" cancels leaving one equation for x.

**decoy808** · November 30th 2009, 12:08 PM

okey i got

x= 11/17
y= 41/17

is this correct?

**masters** · November 30th 2009, 12:58 PM

Originally Posted by decoy808

okey i got

x= 11/17
y= 41/17

is this correct?

[1] $\boxed{y = 4x-5}$

Now, determine the equation of the line perpendicular to [1] through (1, 2) having a slope of -1/4.

$y=mx+b$ where y = 2, x = 1, m= -1/4

$2=-\frac{1}{4}(1)+b$

$8=-1+4b$

$9=4b$

$b=\frac{9}{4}$

[2] $\boxed{y=-\frac{1}{4}x+\frac{9}{4}}$

Solve the system [1] and [2].

Your solution is incorrect. Check it again.

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