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Write the equation of the line in slope intercept form that passes through the point (3,2) and the the intersection of lines: 2x-3y=24 and 2x+y=8

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ANSWER

[tex] \boxed {y = - 2x + 7}[/tex]

EXPLANATION

We want to write the equation in slope-intercept form for the line that passes through the point (3,2) and the intersection of the lines:

[tex]2x - 3y = 24...(1)[/tex]

[tex]2x + y = 8...(2)[/tex]

We subtract equation (1) from equation (2) to get,

[tex]y - - 3y = 8 - 24[/tex]

[tex]4y = - 16[/tex]

[tex]y = - 4[/tex]

Put y=-4 into equation (2) to get the value of x.

[tex]2x - 4 = 8[/tex]

[tex]2x = 8 + 4[/tex]

[tex]2x = 12[/tex]

[tex]x = 6[/tex]

Therefore the line passes through (3,2) and

(6,-4).

The slope of this line is

[tex]m = \frac{ - 4 - 2}{6 - 3} = \frac{ - 6}{3} = - 2[/tex]

The slope intercept form is given by the formula,

[tex]y = mx + c[/tex]

where m=-2 is the slope.

We substitute the slope to get,

[tex]y = - 2x + c[/tex]

We substitute the point (3,2) to find the value of c.

[tex]3 = - 2(2) + c[/tex]

[tex]3 = - 4 + c[/tex]

[tex]c = 4 + 3 = 7[/tex]

Hence the equation in slope-intercept form is

[tex]y = - 2x + 7[/tex]

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