Answer:
Slope-Intercept form: y=3x+7
Standard form: 3x-y=-7
Point-slope form: y-1=3(x+2)
Step-by-step explanation:
Slope-Intercept form:
First, find the slope, using the formula: [tex]m=\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
Our x₁ and y₁ will be the point (-2,1) and our x₂ and y₂ wwill be the point (1,10).
So let's write those in our equation to find slope:
[tex]m=\frac{10-1}{1-(-2)}=\frac{9}{3}=3[/tex]
Therefore, our slope is 3.
Now let's write our linear equation with what we have already in slope-intercept form:
y=3x+b
Well, we still need to find the y-intercept, or "b".
Plug in one of your points for the x and y values of the equation. We'll use the point (-2,1)
[tex]y=3x+b\\1=3(-2)+b\\1=-6+b\\1+6=-6+6+b\\7=b[/tex]
This means our y-intercept is 7. Now we can write our equation in slope-intercept form completely:
y=3x+7
Standard form:
Now, let's find this equation is standard form.
Take your equation in slope-intercept form and write it out again:
[tex]y=3x+7[/tex]
Now, standard form of a linear equation is ax+by=c, so subtract 3x from both sides:
[tex]y-3x=3x-3x+7\\-3x+y=7[/tex]
The "a" coefficient in standard form cannot be negative, so divide the entire equation by -1:
[tex]\frac{-3x+y}{-1}=\frac{7}{-1}\\3x-y=-7[/tex]
Therefore, your equation in standad form is:
3x-y=-7
Point-Slope form:
The formula for point-slope form is y-y₁=m(x-x₁). We already know that our x₁ and y₁ is the point (-2,1) and we know that our slope, m, is 3, so we just have to plug then in where the fit in the equation.
x₁ is -2 and y₁ is 1 and m is 3, so:
y-1=3(x-(-2)) or y-1=3(x+2)
That means our equation in point-slope form is:
y-1=3(x+2)
