Answer:
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An equation is formed when two equal expressions. The equation of the line passing through the intersection and the point (-5,2) is y=(-0.3781)x+ 0.1092.
A line is a one-dimensional shape that is straight, has no thickness, and extends in both directions indefinitely. The equation of a line is given by,
y =mx + c
where,
x is the coordinate of the x-axis,
y is the coordinate of the y-axis,
m is the slope of the line, and
c is the y-intercept.
Given the two equations x + 3y=0 and 4x − 4y −13=0. The intersection of the equation can be found as,
Solve the first equation for x,
x+ 3y = 0
x = -3y
Solve the second equation, by substituting,
4x − 4y −13=0
4(-3y) − 4y −13=0
-12y - 4y -13 = 0
-16y = 13
y = 13/(-16)
y = -0.8125
Substitute the value of x,
x = -3y
x = -3(-13/16)
x = 39/16
x = 2.4375
Hence, the coordinate of the point of intersection is (2.4375, -0.8125).
Now, the slope of the line passing through the intersection and the point (-5,2) is,
Slope, m = (2 + 0.8125)/(-5-2.4375)
= -2.8125/7.4375
= -0.3781
Substitute the slope and the coordinate in the equation of the line,
y = mx + c
2 = (-0.3781)(-5) + c
2 - 1.89 = c
c = 0.1092
Hence, the equation of the line passing through the intersection and the point (-5,2) is y=(-0.3781)x+ 0.1092.
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