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Determine the equation of the line.

​(Type an equation. Simplify your answer. Type your answer in​ slope-intercept form.)

Due In 30 Minutes Determine The Equation Of The Line Type An Equation Simplify Your Answer Type Your Answer In Slopeintercept Form class=

Sagot :

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Answer:

y = 6x - 12

Step-by-step explanation:

In order to find the equation of the line in slope-intercept form, y = mx + b, we need to find the slope and the y-intercept of the given graph.

Given points (2, 0) and (0, -12)

Let (x1,y1) = (2, 0)

(x2, y2) = (0, -12)

We can use the following slope formula to find the slope of the line:

m = (y2 - y1)/(x2 - x1)

m = (-12 - 0)/(0 - 2)

m = -12/ -2

m = 6

Therefore, the slope (m) of the line is 6.

Next, we need to determine the y-intercept of the line. The y-intercept is the point on the graph where it crosses the y-axis, and has the coordinate (0, b). If you look at the graph, the line crosses at point (0, -12), which is also on of the points that we used earlier to solve for the slope. The y-coordinate of (0, -12) is the y-intercept (b). Thus, the y-intecept (b) = -12.  

Therefore, the linear equation of the given graph is:

y = 6x - 12

Take 2 points

  • (0,-12)
  • (4,12)

Slope:-

[tex]\ \ \sf\longmapsto m=\dfrac{12+12}{4}=\dfrac{24}{4}=6[/tex]

Equation of line in point slope form

[tex]\ \ \sf\longmapsto y-y_1=m(x-x_1)[/tex]

[tex]\ \ \sf\longmapsto y+12=6(x)[/tex]

[tex]\ \ \sf\longmapsto 6x-y-12=0[/tex]

  • Convert to slope intercept form y=mx+b

[tex]\ \ \sf\longmapsto y=6x-12[/tex]

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