An equation of the line that is parallel to the given line and passes through the point (−3, 2) is: 4x + 3y = -6.
How to calculate the slope of a straight line?
Mathematically, the slope of any straight line can be calculated by using this formula;
Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)
Slope, m = (y₂ - y₁)/(x₂ - x₁)
By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:
Points (x, y) = (3, -1)
Points (x, y) = (0, 3)
Substituting the given parameters into the formula, we have;
Slope, m = (3 + 1)/(0 - 3)
Slope, m = 4/-3
Slope, m = -4/3.
In Geometry, two (2) lines are parallel under the following conditions:
m₁ = m₂ ⇒ -4/3 = -4/3
Note: m represents the slope.
At point (-3, 2), an equation of the other line can be calculated by using the point-slope form:
y - y₁ = m(x - x₁)
Where:
- m represents the slope.
- x and y are the points.
Substituting the given points into the formula, we have;
y - y₁ = m(x - x₁)
y - 2 = -4/3(x - (-3))
y - 2 = -4/3(x + 3)
y - 2 = -4x/3 - 4
y - 2 = -4x/3 - 4 + 2
y = -4x/3 - 2
Multiplying all through by 3, we have:
3y = -4x - 6
Rearranging the equation, we have:
4x + 3y = -6
Read more on slope here: brainly.com/question/3493733
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