DrDelMath

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1. Write the equation of the line with slope 5 and y-intercept 2 in slope intercept form.
Use the slope-intercept formula y = mx + b with m = 5 and b = 2 to obtain y = 5x + 2 as the desired equation.

2. Write the equation of the line through the point (3,5) with slope 2.
Use the point-slope formula with m = 2, x₁ = 3 and y₁ = 5 to obtain y - 5 = 2(x - 3) = 2x - 6.
To write the equation y - 5 = 2x - 6 in slope-intercept form, add 5 to both sides to obtain y = 2x - 1 as the desired equation.

3. Write the equation of the line through the points (3, 2) and (-2, 7). Write the equation in in slope intercept form.
Use to calculate the slope of the line through the two points.

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Now use the point-slope formula with m = -1, x₁ = 3 and y₁ = 2 to obtain y - 2 = (-1)(x - 3) = -x + 3.
Finally rewrite the equation in slope-intercept form by adding 2 to both sides of y - 2 = -x + 3 to obtain y = -x + 5 as the desired equation.

4. Write the equation of the line 2x - 3y = 12 in slope-intercept form.
2x - 3y = 12     Add -2x to both sides
-3y = -2x + 12     Multiply both sides by -1/3
y = x + 4

5. Determine the inequality whose graph is the half-plane bounded by the line through (2, 1) and (4, -3) and containing the point (2, 3). Write the inequality in both standard form and slope-intercept form.
Use the formula for slope