Write the equation of the line in slope-intercept form, slope is 5 and (2,6) is on the line

Mathematics

2 answers:

Diano4ka-milaya [45]3 years ago

6 0

slope-intercept form:

y = mx + b where m = slope and b = y intercept

given slope m = 5 , now you need to find b

passing thru (2,6)

using y = mx + b to find b

y = mx + b

b = y - mx

b = 6 - (5)(2)

y = 6 - 10

y = -4

Now you know m = 5 and b = -4

Equation:

y = 5x - 4

jeyben [28]3 years ago

4 0

$\bf (\stackrel{x_1}{2}~,~\stackrel{y_1}{6})\qquad \qquad \qquad 
slope = m\implies 5
\\\\\\
% point-slope intercept
\stackrel{\textit{point-slope form}}{y- y_1= m(x- x_1)}\implies y-6=5(x-2)
\\\\\\
y-6=5x-10\implies y=5x-4$

You might be interested in

Find the equation of a straight line passing throught the point listed and having the given gradient. Express your answer in the

Igoryamba

First let's try to find the equation in this form : y = mx + c

The gradient is given 3 . In a line's equation, x's coefficient represents the line's gradient.

So equation of a line with the gradient of 3, would look like this ;

 $y= 3x + c$

Now a point that the line passes through is given, (1, 2)

This point's x-coordinate is 1 and y-coordinate is 2.

So we'll plug its x-coordinate value in the equation and also y-coordinate value. So we can solve it.

As you know, $x=1$ and $y=2$

$y = 3x + c$

$2\quad =\quad 3\cdot 1+c\\ \\ 2\quad =\quad 3+c\\ \\ 2-3\quad =\quad c\\ \\ -1\quad =\quad c$

We found c = -1

Also in a line's equation, c is constant and it represents the line's y-intercept

So let's build the line's equation.

$m=3$ and $c=-1$

$y= mx + c$

$y= 3x -1$

We found the line's equation in this form, $y= mx + c$

Now let's turn it into this form, $ax + by + c = 0$

$y\quad =\quad 3x-1\\ \\ y-3x\quad =\quad -1\\ \\ y-3x+1\quad =\quad 0\\ \\ -3x+y+1\quad =\quad 0$

Final answers,

$\boxed { y\quad =\quad 3x-1 }$

and

$\boxed { -3x+y+1\quad =\quad 0 }$

I hope this was clear enough :)

5 0

3 years ago

Read 2 more answers

Which model shows 1/2 times 1/3

arlik [135]

Answer:

Where's the model?

7 0

2 years ago

Read 2 more answers

The area of a rectangular of length L width W is given by the formula A =LW. Ann's backyard is rectangular with a length of 27.6

marta [7]