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Answer:
Please check the explanation.
Step-by-step explanation:
Given the points
Finding the slope between (-1, -2) and (2, 4)
[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]\left(x_1,\:y_1\right)=\left(-1,\:-2\right),\:\left(x_2,\:y_2\right)=\left(2,\:4\right)[/tex]
[tex]m=\frac{4-\left(-2\right)}{2-\left(-1\right)}[/tex]
[tex]m=2[/tex]
Using the point-slope form
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 2 and the point (-1, -2)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
[tex]y -(-2) = 2(x-(-1)[/tex]
Thus, the point-slope form of the line equation is
[tex]y -(-2) = 2(x-(-1)[/tex]
now, write the slope-intercept form of the line equation y = mx+b
[tex]y-\left(-2\right)=2\left(x-\left(-1\right)\right)[/tex]
[tex]y+2=2\left(x+1\right)[/tex]
subtract 2 from both sides
[tex]y+2-2=2\left(x+1\right)-2[/tex]
Simplify
[tex]y=2x+0[/tex]
[tex]y = 2x[/tex]
Therefore, the equation in slope-intercept form is: