Find the Linear Equation Through Points (-2,-6) and (4,12): Two-Point Form

Find the equation of the line passing through the two points (−2,−6),(4,12) (-2,-6),(4,12)

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the algebraic representation of the function
00:04 Use the formula to find the slope using 2 points
00:11 In each point, the left number represents X-axis and the right Y
00:17 Plot the points according to the data and find the slope
00:30 This is the line's slope
00:35 Now use the line equation
00:39 Plot the point according to the data
00:44 Input the slope, and solve to find the intersection point (B)
00:59 Isolate the intersection point (B)
01:05 This is the intersection point with the Y-axis
01:11 Now input the intersection point and slope into the line equation
01:19 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Find the equation of the line passing through the two points (−2,−6),(4,12) (-2,-6),(4,12)

2

Step-by-step solution

In the first step, we'll find the slope using the formula:

m=y2−y1x2−x1 m=\frac{y_2-y_1}{x_2-x_1}

We'll substitute according to the given points:

m=12−(−6)4−(−2) m=\frac{12-(-6)}{4-(-2)}

m=186=3 m=\frac{18}{6}=3

Now we'll choose the point (4,12) and use the formula:

y=mx+b y=mx+b

12=3×4+b 12=3\times4+b

12=12+b 12=12+b

b=0 b=0

We'll substitute the data into the formula to find the equation of the line:

y=3x y=3x

3

Final Answer

y=3x y=3x

Practice Quiz

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What is the solution to the following inequality?

\( 10x-4≤-3x-8 \)

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