Answer:
y= 3x +1
Step-by-step explanation:
Let's write the equation of the line in slope-intercept form. That is, y= mx +c, where m is the slope and c is the y-intercept.
Start by finding the slope with the formula below:
[tex]\boxed{\text{slope}=\frac{y_1-y_2}{x_1-x_2} }[/tex]
Slope
[tex]=\frac{10-(-2)}{3-(-1)}[/tex]
[tex]=\frac{10+2}{3+1}[/tex]
[tex]=\frac{12}{4}[/tex]
= 3
Substitute m= 3 into the equation:
y= 3x +c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= -2,
-2= 3(-1) +c
-2= -3 +c
c= -2 +3
c= 1
Thus, the equation of the line is y= 3x +1.
_______
Alternatively, we can write the equation in the point-slope form.
[tex]\boxed{y-y_1=m(x-x_1)}[/tex]
Substitute m= 3 and a pair of coordinates into [tex](x_1,y_1)[/tex]:
y -10= 3(x -3)
Additional:
For more questions on writing equations of line, check out:
The equation which passes through the points (-1,-2)and(3,10) will be y= 3x +1
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
Let's write the equation of the line in slope-intercept form. That is, y= mx+c, where m is the slope and c is the y-intercept.
Start by finding the slope with the formula below:
[tex]\rm Slope =\dfrac{y_1-y_2}{x_1-x_2}[/tex]
Slope
[tex]\rm Slope =\dfrac{10-(-2)}{3-(-1)}[/tex]
[tex]\rm Slope=\dfrac{12}{4}[/tex]
Slope = 3
Substitute m= 3 into the equation:
y = 3x + c
To find the value of c, substitute a pair of coordinates into the equation.
When x= -1, y= -2,
-2 = 3(-1) + c
-2= -3 + c
c = -2 + 3
c = 1
Thus, the equation of the line is y = 3x + 1.
Alternatively, we can write the equation in the point-slope form.
y - y₁ = m ( x - x₁ )
Substitute m= 3 and a pair of coordinates into :
y - 10 = 3 ( x - 3 )
Therefore the equation which passes through the points (-1,-2)and(3,10) will be y= 3x +1
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