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Sagot :
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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