The equation in standard form that has a graph that passes through the point (-4,2) and a slope of 9/2 is 9x - 2y = -40
The equation in slope-intercept form of the line that passes through the point (2,-2) and is perpendicular to the line represented by y=2/5x+2 is
[tex]y = \frac{-5}{2}x + 3[/tex]
The point-slope form of the equation of a line is:
[tex]y-y_1=m(x-x_1)[/tex]
Substitute x₁ = -4, y₁ = 2, and the slope, m = 9/2 into the equation
[tex]y - 2 = \frac{9}{2} (x - (-4))\\\\y - 2 = \frac{9}{2} (x + 4)\\\\[/tex]
Cross multiply:
2(y - 2) = 9(x + 4)
Expand the equation using the distributive rule
2y - 4 = 9x + 36
Collect like terms
9x - 2y = -4 - 36
9x - 2y = -40
2) The given equation is:
[tex]y = \frac{2}{5}x + 2\\\\[/tex]
The slope, m = 2/5
The equation perpendicular to y = mx + c is:
[tex]y - y_1 = \frac{-1}{m}(x - x_1)[/tex]
The line passes through the point (2, -2)
Substitute x₁ = 2, y₁ = -2, and m = 2/5 into the equation above
[tex]y - (-2) = \frac{-5}{2} (x - 2)\\\\y+2 = \frac{-5}{2} (x - 2)\\\\y+2 = \frac{-5}{2}x + 5\\\\y = \frac{-5}{2}x + 5-2\\\\y = \frac{-5}{2}x + 3[/tex]
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