# Equation Of The Line?

• Sep 11th 2011, 05:52 AM
MathsFreakLove
Equation Of The Line?
hi im new on here, (Hi)

i have two questions i am stuck on and would like your help :

here are the qestions:

1.the line y=1/4 x +2 meets the y axis at the point B. the point C has co ordinates (-5,3). find the gradient of the line joining points B and C .

2.the lines y= x and y=2x-5 intersect at the point A . find the equation of the line with gradient 2/5 that passes through the point A . ( Hint : solve y=x and y= 2x-5 simultaneously.)

thank you
• Sep 11th 2011, 06:20 AM
Prove It
Re: Equation Of The Line?? Help Please!
Quote:

Originally Posted by MathsFreakLove
hi im new on here, (Hi)

i have two questions i am stuck on and would like your help :

here are the qestions:

1.the line y=1/4 x +2 meets the y axis at the point B. the point C has co ordinates (-5,3). find the gradient of the line joining points B and C .

2.the lines y= x and y=2x-5 intersect at the point A . find the equation of the line with gradient 2/5 that passes through the point A . ( Hint : solve y=x and y= 2x-5 simultaneously.)

thank you

1. What is the y intercept of $\displaystyle \displaystyle y = \frac{1}{4}x + 2$? How do you find the gradient of a line that passes through two points?
• Sep 11th 2011, 06:28 AM
skeeter
Re: Equation Of The Line?? Help Please!
Quote:

Originally Posted by MathsFreakLove
i have two questions i am stuck on and would like your help :

here are the qestions:

1.the line y=1/4 x +2 meets the y axis at the point B. the point C has co ordinates (-5,3). find the gradient of the line joining points B and C .

point B is the y-intercept of the line ... you should be able to recognize that value since the line's equation was given in slope-intercept form.

once you determine the coordinates of the y-intercept, use the equation to determine the slope between two points in the x-y plane.

$\displaystyle m = \frac{y_2-y_1}{x_2-x_1}$

2.the lines y= x and y=2x-5 intersect at the point A . find the equation of the line with gradient 2/5 that passes through the point A . ( Hint : solve y=x and y= 2x-5 simultaneously.)

set x = 2x-5 to determine the x-value of intersection, then use either line to determine the y-value of intersection. once you get those coordinates, use the point-slope form of a linear equation to find the desired equation ...

$\displaystyle y - y_1 = m(x - x_1)$ , where $\displaystyle (x_1,y_1)$ is the point of intersection and $\displaystyle m$ is the given slope.

let's see what you can do