How do you write the equation in point slope form given (3,5) and (8,15)?

3 Answers
Apr 13, 2018

y=2x-1y=2x1

Explanation:

First, we have to solve for the slope using this equation:

m = (y_2-y_1)/(x_2-x_1)m=y2y1x2x1

This formula makes sense because slope is rise over run. Rise being the yy values and run being the xx values.

Now you choose which point is point 2 (includes y_2y2 and x_2x2) and which point is point 1 (includes y_1y1 and x_1x1)

Point 2: (3,5)->y_2 = 5(3,5)y2=5 and x_2 =3x2=3
Point 1: (8,15)->y_1 = 15(8,15)y1=15 and x_1 = 8x1=8

Plug into the formula and solve for the slope:

m = (5-15)/(3-8)m=51538

m = (-10)/(-5)m=105

m = (10)/(5)m=105

m=2m=2

Now we know that the slope, m=2m=2

Next, we have to use point-slope formula to get the equation:

y-y_1=m(x-x_1)yy1=m(xx1)

You can plug in either point for the x_1x1 and y_1y1 values. Let's use the point (3,5)(3,5).

y-5=m(x-3)y5=m(x3)

Now plug in the slope

y-5=2(x-3)y5=2(x3)

Distribute the 22

y-5=2x-6y5=2x6

Add 55 to both sides

y-5+5=2x-6+5y5+5=2x6+5

y=2x-1y=2x1

Final Answer:

y=2x-1y=2x1

Apr 13, 2018

color(indigo)(y - 5 = 2*(x - 3) " is the point - slope form of equation"y5=2(x3) is the point - slope form of equation

Explanation:

If two points on a line are known, we can use the following formula to write the equation :

(y - y_1) / (y_2 - y_1) = (x - x_1) / (x_2 - x_1)yy1y2y1=xx1x2x1

"Given : (x_1, y_1) = (3,5), (x_2,y_2) = (8,15)Given:(x1,y1)=(3,5),(x2,y2)=(8,15)

Hence, equation of the line is

(y - 5) / (15-5) = (x - 3) / (8 - 3)y5155=x383

(y-5) / cancel(10)^color(red)(2) = (x - 3) / cancel 5

color(purple)(y - 5 = 2*(x - 3)

Standard form of Point-Slope equation is

y - y_1 = m * (x - x_1)

Apr 13, 2018

Equation of the line in Slope-Intercept Form: color(green)(y=2x-1

Explanation:

If the slope (m) of a line and the coordinate (x_1, y_1) of one end-point of the line is known, we can write the equation of the line in Point-Slope Form:

color(red)(y-y_1=m(x-x_1)

To find the slope if we are given two end-points of a line, we use the formula:

color(blue)(Slope(m)=(y_2-y_1)/(x_2-x_1)

We are given the points: (3,5) and (8,15)

Note that x_1 = 3; y_1=5; x_2=8 and y_2=15

Slope(m)=(15-5)/(8-3)

rArr m=10/5

rArr Slope(m)=2

Next, consider the equation of the point-slope form.

Consider the point (3,5)

We also found that Slope(m)=2

x_1=3 and y_1=5

y-y_1=m(x-x_1)

rArr y-5=2(x-3)

rArr y-5=2x-6

Add 5 to both sides of the equation.

rArr y-5+5=2x-6+5

rArr y-cancel 5+cancel 5=2x-6+5

rArr color(green)(y=2x-1

This is the required equation in the Point-Slope Form.

We can also graph the line and find the intercepts.

Substitute y=0 to obtain the x-intercept.

2x-1=0

Add 1 to both sides.

rArr 2x-1+1=0+1

rArr 2x-cancel 1+cancel 1=0+1

rArr 2x = 1

Divide both sides by 2

(2x)/2=1/2

(cancel 2x)/cancel 2=1/2

x=1/2

x=0.5

Hence (0.5,0) is the x-intercept.

Substitute x=0 to obtain the y-intercept.

y=2(0)-1

y=0-1

y=-1

Hence (0,-1) is the y-intercept.

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