The required equation in slope-intercept form is y = - [tex]\frac{2}{3}[/tex]x + 4
What is an equation?
An equation represents any two expressions or statements are equal that means they are having an equal to (=) sign in brtween them.
What is slope intercept form?
The equation of a straight line in the form y = mx + b where m is the slope of the line and b is its y-intercept is called slope-intercept form of the equation.
How to find the slope ?
Slope of a line is the inclination of the straight line towards x axis.
- If a straight line passes through two points (a , b) and (c , d), then slope(m) of the straight line can be calculated by the formula,
[tex]m = \frac{d - b}{c-a}[/tex]
According to the problem, the straight line passes through (6 , 0) , (3 , 2) , (0, 4) , (-3 , 6).
Slope (m) = [tex]\frac{2-0}{3-6}[/tex] = - [tex]\frac{2}{3}[/tex]
How to write the equation in slope-intercept form?
The equation can be written as
y = - [tex]\frac{2}{3}[/tex]x + b
- Now , this line passes thorugh (0,4).
- So, (0,4) will satisfy the equation
∴ putting (0,4) in the equation, we get,
y = 4
∴ The required equation is y = - [tex]\frac{2}{3}[/tex]x + 4.
- For check we can satisfy the point ( -3 , 6) in the equation.
- [tex]\frac{2}{3}[/tex](-3) + 4 = 6
CLearly, the point satisfies the equation.
So, the equation y = - [tex]\frac{2}{3}[/tex]x + 4 is correct
Find out more information about equations in slope-intercept form here: https://brainly.com/question/1884491
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